Tristan Gillard

Jean Lieber

Emmanuel Nauer

Improving adaptation knowlege discovery by exploiting negative cases

Keywords: adaptation knowledge discovery, closed itemset extraction, negative cases, case-based reasoning

Case-based reasoning usually exploits positive source cases consisting in a source problem and its solution that is known to be a correct for the problem. The work presented in this paper addresses in addition of positive case exploitation, the exploitation of negative cases, i.e. problem-solution pairs where the solution is an incorrect answer to the problem, which can be acquired when the case-based reasoning (CBR) process fails. An originality of this work is that positive and negative cases are used both for adaptation knowledge (AK) discovery using closed itemsets built on variations between cases. Experiments show that exploiting negative cases in addition to positive ones improves the quality of the AK being extracted and, so, improves the results of the CBR system.

The paper is organized as follows. Section 2 introduces the motivations and the preliminaries for this work, introducing CI extraction and CBR with related work. Section 3 describes our approach for exploiting positive and negatives cases in an AK discovery process. Section 4 presents the evaluation of our approach through experiments and discusses the results. Section 5 points out lines for future research.

Motivation and preliminaries

Cooking CBR systems, as the ones which have participated to the Computer Cooking Contest (e.g. TAAABLE [START_REF] Cordier | Taaable: a Case-Based System for personalized Cooking[END_REF]) are typical of systems that are concerned by the objective of this work. Indeed, it has been showed that adaptating cooking recipes takes benefit from the use of AK [START_REF] Gaillard | Adaptation knowledge discovery for cooking using closed itemset extraction[END_REF]. Moreover, feedback may be collected about the system results. For example, the TAAABLE system provides a result interface allowing the users to evalauate whether a recipe adaptation is correct or not [START_REF] Skaf-Molli | Knowledge Continuous Integration Process (K-CIP)[END_REF]. This approach to manage correct and uncorrect adaptations is a way to collect positive and negative cases, which can both be stored in the case base (with an appropriate label).

Itemset extraction

Itemset extraction is a collection of data-mining methods for extracting regularities into data, by aggregating object items appearing together. Like FCA [START_REF] Ganter | Formal Concept Analysis: Mathematical Foundations[END_REF], itemset extraction algorithms start from a formal context K, defined by K = (G, M, I), where G is a set of objects, M is a set of items, and I is the relation on G × M stating that an object is described by an item [START_REF] Ganter | Formal Concept Analysis: Mathematical Foundations[END_REF]. Table 1 shows an example of context, in which 4 recipes are described by the ingredients they require: G is a set of 4 objects (recipes r 1 , r 2 , r 3 , and r 4 ), M is a set of 5 items (ingredients Apple, PieCrust, PuffPastry, Sugar, and Cream).

An itemset I is a set of items, and the support of I, supp(I), is the number of objects of the formal context having every item of I. I is frequent, with respect to a threshold σ, whenever supp(I) ≥ σ. I is closed if it has no proper superset J (I J) with the same support. For example, {Apple, PieCrust} is an itemset and supp({Apple, PieCrust}) = 2 because exactly 2 recipes require both Apple and PieCrust. However, {Apple, PieCrust} is not CI, because {Apple, A p p l e P i e C r u s t P u f f P a s t r y S u g a r C r e a m A p p l e - A p p l e = A p p l e + P i e C r u s t - P i e C r u s t = P i e C r u s t + P u f f P a s t r y - P u f f P a s t r y = P u f f P a s t r y + S u g a r - S u g a r = S u g a r

r 1 × × × r 2 × × × × r 3 × × × r 4 × ×
+ C r e a m - C r e a m = C r e a m + V R 1 ,R 2 × × × × V R 1 ,R 3 × × × × × V R 1 ,R 4 × × × × ×
Table 2: Formal context for ingredient variations in pairs of recipes (r 1 , r 2 ), (r 1 , r 3 ) and (r 1 , r 4 ).

PieCrust, Sugar} has the same support. For σ = 2, the frequent CIS (FCIS) of this context are {Apple, PieCrust, Sugar} and {Sugar, Cream}.

For our experiments, we use CORON [START_REF] Szathmary | CORON: A Framework for Levelwise Itemset Mining Algorithms[END_REF] a software platform which implements efficient algorithms for symbolic data mining and especially FCI computation.

Exploiting case variations for AK discovery

Exploiting case variations is not a new idea. [START_REF] Hanney | Learning adaptation rules from a case-base[END_REF] introduces this approach of AK learning based on pairwise comparisons of cases. This approach has been applied in various domains such as chemistry [START_REF] Berasaluce | An Experiment on Mining Chemical Reaction Databases[END_REF], medicine [START_REF] D'aquin | Case base mining for adaptation knowledge acquisition[END_REF] or cooking [START_REF] Badra | Opportunistic Adaptation Knowledge Discovery[END_REF][START_REF] Gaillard | Adaptation knowledge discovery for cooking using closed itemset extraction[END_REF].

For an ordered pair of cases (c 1 , c 2 ), the approach consists in representing what features have to be removed (-), kept (=) and added (+) to transform c 1 into c 2 . For example, for a pair (r i , r j ) of recipes described each by the ingredients they require, the representation of the variation is denoted by V ij , where V ij represents the variation of ingredients between r i and r j . Each ingredient ing is marked by -, =, or +:

-ing -∈ V ij if ing is an ingredient of r i but not of r j . -ing + ∈ V ij if ing is an ingredient of r j but not of r i . -ing = ∈ V ij if
ing is an ingredient of both r i and r j .

Table 2 shows the ingredient variations for 3 ordered pairs of recipes described in Table 1. An AK discovery process based on FCIS can be run on such a binary table which constitutes a formal context. Each extracted FCI produces an adaptation rule ar with a support supp(ar), i.e. the number of V ij containing ar. For example, for σ = 2, {PieCrust-, PuffPastry+} is an FCI which produces an adaptation rule consisting in replacing the pie crust by a puff pastry.

Assumptions and notations about CBR

Let P and S be two sets. A problem (resp., a solution) is an element of P (resp., of S). The existence of a binary relation with the semantics "has for solution" is assumed. In this paper, this relation is assumed to be functional, guided by the idea to fully automatize the evaluation process; let f be the function from P to S such that y = f(x) if y is the solution of x. A case is a pair (x, y) ∈ P × S where y = f(x).

A CBR system on (P, S, f) is built with a knowledge base KB = (CB, DK, RK, AK) where CB is a finite set of cases, DK is the domain knowledge, RK is the retrieval knowledge (in this work, RK = dist, a distance function on P), and AK is the adaptation knowledge that will take the form of adaptation rules.

A CBR system on (P, S, f) aims at associating to a query problem x tgt a y tgt ∈ S, denoted by y tgt = f CBR (x tgt ). The function f CBR is intended to be an approximation of f. It is built thanks to the following functions:

the retrieval function, with the profile retrieval : x tgt → (x s , y s ) ∈ CB; the adaptation function, with the profile adaptation : ((x s , y s ), x tgt ) → y tgt ∈ S; it is usually based on DK and AK. ((x s , y s ), x tgt ) is an adaptation problem.

Thus f CBR (x tgt ) = adaptation(retrieval(x tgt ), x tgt ).

With no domain and adaptation knowledge (DK = AK = ∅), the adaptation consists usually of a mere copy of the solution. This process is called null adaptation: null_adaptation : ((x s , y s ), x tgt ) → y s Adaptation principle using adaptation rules. Generally speaking, an adaptation rule ar is a function mapping an adaptation problem ((x s , y s ), x tgt ) ∈ CB × P to y tgt ∈ S∪{failure}. Two cases of failure (y tgt = failure) are considered: (i) no (x s , y s ) ∈ CB} such as dist(x s , x tgt ) ≤ σ, with σ a given threshold, is returned by the retrieval function, and (ii) no AR ar is applicable on this adaptation problem. Else, y tgt is a proposed solution to x tgt , by adaptation of (x s , y s ) according to ar. A score supp(ar) ≥ 0 is associated with a rule ar; the higher is supp(ar), the more ar is preferred.

The adaptation consists in selecting the subset AAR of AK of applicable adaptation rules with maximum support: ar ∈ AAR iff ar((x s , y s ), x tgt ) = failure and there exists no ar ∈ AAR such that supp(ar ) > supp(ar).

Boolean setting

We presented at the beginning of section 2 the interest of AK discovery for a real life application. However, evaluating how an AK approach improves the results of the CBR system in such a concrete application is difficult because experiments require humans (users or experts) who have to evaluate the quality or the validity of the system answers (see for example [START_REF] Gaillard | How Managing the Knowledge Reliability Improves the Results of a Reasoning Process[END_REF] where the evaluation process implies users who have to judge if the TAAABLE cooking system returns correct or incorrect answers in the context of collaborative knowledge acquisition). Such a human based evaluation has many inconvenients: (a) specific interfaces have to be built to guarantee a blind evalution, (b) it is time consuming, especially comparing to an automated evaluation, (c) it requires available users and/or experts, and (d) the coverage of the evaluation is limited because of points (b) and (c).

For these reasons, we use in this work a Boolean setting in which all experiments can be automatized using Boolean functions as f. Let m, n ∈ N * , P = B m , S = B n and f : P → S, be a boolean function to be approximated. A CBR system is considered on (P, S, f) with DK = ∅, RK = dist, the Hamming distance on P, and AK a set of adaptation rules.

Adaptation rule language. The adaptation rule language used in this work is based on the notion of variations between Booleans, as described hereafter. Given , r ∈ B ( stands for left, r for right), the variation from to r is represented by variation symbols. Each of the 4 ordered pairs ( , r) is represented by a primary variation symbol v:

-( , r) = (1, 0) is represented by v = -; -( , r) = (0, 1) is represented by v = +; -( , r) = (0, 0) is represented by v = 0; -( , r) = (1, 1) is represented by v = 1.
Each primary variation symbols is linked to 3 inferred variation symbols. Fig. 1 shows the generalization links between the primary variation symbols and the inferred ones. For example, v =is linked to =, stating that = r, to =1 and to r=0, stating that (resp. r) is equal to 1 (resp. 0).

Given two cases c 1 = (x 1 , y 1 ) and c 2 = (x 2 , y 2 ), the variation V 12 from c 1 to c 2 is encoded by the set of the expressions x v i and y w j such that v (resp., w) is a variation symbol from x 1 i to x 2 i (resp., from y 1 j to y 2 j ). For example, if (x 1 , y 1 ) = ((0, 1), 0) and (x 2 , y 2 ) = ((0, 0), 1) then

V 12 = {x =0 1 , x = 1 , x =0 1 , x r=0 1 , x - 2 , x = 2 , x =1 2 , x r=0 2 , y + 1 , y = 1 , y =0 1 , y r=1 1 }.
An adaptation rule ar is a set of expressions x v i and y w j . It is applicable on an adaptation problem ((x s , y s ), x tgt ) if there exists y tgt ∈ B n such that V st ⊇ ar (where V st represents the variation from (x s , y s ) to (x tgt , y tgt )). If it is applicable, then its application consists in choosing such a y tgt . If several y tgt 's exist, the chosen one is the closest to y s according to the Hamming distance on S = B n , meaning that if ar gives no constraint on some y tgt j then y tgt j = y s j . For example:

if ar = {x - 1 , x = 2 , y + 1 }, (x s , y s ) = ((1, 0, 0), (0, 0)) and x tgt = (0, 0, 1) then ar is applicable on ((x s , y s ), x tgt ) and ar((x s , y s ), x tgt ) = y tgt = (1, 0) An originality of this work is to build an AK discovey for CBR exploiting both positive and negative source cases. For a case c = (x, y) ∈ CB, the case c is said positive if y = f(x) and negative if y = f(x). We denote CB + (resp. CB -), the set of positive (resp. negative) cases of CB, with CB = CB + ∪ CB -.

Starting from the two sets of cases CB + and CB -, ordered pairs of cases (c 1 , c 2 ) are formed, with c 1 = (x 1 , y 1 ) ∈ CB + and c 2 = (x 2 , y 2 ) ∈ CB such that x 1 = x 2 . Each such pair is encoded by a set V 12 of the variations from x 1 i to x 2 i and from y 1 j to y 2 j , as presented before. When c 2 ∈ CB + , the variations between c 1 and c 2 can be considered as a positive example of AR (i.e. the application of the AR will produce a correct answer). When c 2 ∈ CB -, the variations between c 1 and c 2 can be considered as a negative example of AR (i.e. the application of AR will produce an incorrect answer).

Exploiting positive examples

The AR learning process based on FCI extraction takes in input a set of V ij , which will be used to build the formal context. In this work and especially for the evaluation, we have used two approaches to build the formal context. The first one consists in using each V ij as an object with only the primary variations as properties. This approach will be noted AK + in the following. The second approach consists in extending AK + by using also the more general variations that can be inferred from the primary ones as object properties. This is a classical AK approach for extracting more general adaptation rules (i.e. rules with a higher support) (e.g. [START_REF] Dufour-Lussier | Improving case retrieval by enrichment of the domain ontology[END_REF]). This second AK approach will be noted AK +I in the following.

Exploiting negative examples

The objective of the AK +I approach is the extraction of more general AR. However, when an AR is too general, its application is likely to give an incorrect answer. This is for example the case when the general rule consisting in replacing a pie crust by a puff pastry is applied to a salted tart recipe. This observation motivates the exploitation of negative examples for filtering too general ARS.

Exploiting negative examples in a learning process requires a specific approach. Some machine learning approaches such as, for example the version space model introduced by Mitchell [START_REF] Mitchell | Version Space: An Approach to Concept Learning[END_REF], considers a training set composed of positive and negative examples in order to learn a binary classification model. The idea of the version space model is to build a space of hypotheses (view a disjunction of logical sentences) such that a hypothesis covers all positive examples and no negative ones. More recently, Ganter and Kuznetsov established the link between the version space model and FCA [START_REF] Ganter | Hypotheses and version spaces[END_REF][START_REF] Kuznetsov | Complexity of learning in concept lattices from positive and negative examples[END_REF]. Our exploitation of negative examples in order to extract ARS is based on the same idea introduced in these related works: generating AR covering positive examples without covering negative ones. A first approach to address this issue consists in generating AR only on a formal context built on positive examples and then removing rules which cover at least one negative example. Let V e - be the set of variations of the negative example e -, ar is removed if e -⊇ ar. However, the complexity of this approach (in O(|AR| × |CB -|)) leads us to consider another more efficient way to compute ARS consistent with negative examples. For this, we take advantage of the efficiency of the FCI extraction algorithms in adding in the formal context the negative examples and by removing, before generating the AR, the CI which extent contains at least one negative example. This appproach exploiting both positive and negative examples (with inferred variations) will be noted AK +-I in the following.

Evaluation

The objective of the evaluation is to study, on various types of Boolean functions, how exploiting negative cases in addition to positive ones improves the results of the CBR system. Experimental results are presented and discussed.

Experiment setting

In the experiment, P = B 8 and S = B, Functions f are randomly generated using the following generators that are based on the three main normal forms, with the purpose of having various types of functions:

CNF f is generated in a conjunctive normal form, i.e., f(x) is a conjunction of n conj disjunctions of literals, for example f(x

) = (x 1 ∨ ¬x 7 ) ∧ (¬x 3 ∨ x 7 ∨ x 8 ) ∧ x 4 .
The value of n conj is randomly chosen uniformly in {3, 4, 5}. Each disjunction is generated on the basis of two parameters, p + > 0 and p -> 0, with p + + p -< 1: each variable x i occurs in the disjunct in a positive (resp. negative) literal with a probability p + (resp., p -). In the experiment, the values p + = p -= 0.1 were chosen. DNF f is generated in a disjunctive normal form, i.e., it has the same form as for CNF except that the connectors ∧ and ∨ are exchanged. The parameters n disj , p + and p - are set in the same way. Pol is the same as DNF, except that the disjunctions (∨) are replaced with exclusive or's (⊕), thus giving a polynomial normal form. The only different parameter is p -= 0 (only positive literals occur in the polynomial normal form).

The case base CB = CB + ∪ CB -is generated randomly, with the values for their sizes:|CB + | ∈ {16, 32, 48}, i.e. |CB + | is between 1 16 and 3 16 of |P| = 2 8 = 256, and

|CB -| ∈ {0, |CB + | 2 , |CB + |}.
Each positive source case (x, y) is generated as follows: x is randomly chosen in P with a uniform distribution and y = f(x). Each negative source case (x 1 , y 1 ) is generated by generating a positive source case (x, y) with an inversion of the solution y: y 1 = ¬y.

Five adaptation approaches are tested: AK + , AK +-, AK +I , AK +-I and N N , the classical nearest neighbour approach with the null_adaptation for adaptation function. The retrieve and adaptation processes attempt to adapt, for N N , the 3 source cases which are the closest to the target problem according to dist with a maximal distance of 2 on P. For the three approaches based on AK, there is no threshold on the prec car maximal distance: all source cases for which AR can be applied participate to solve the problem. A vote on the results computed from the retrieved cases is used to associate a unique element y ∈ S. Moreover, a vote is also used when using AR: 3 ARS with the higher supports are used to adapt each of the source cases and the most frequent result wins. All the approaches are evaluated according to two measures: the precision prec and the correct answer rate car. Let ntp be the number of target problems posed to the system, na be the number of (correct or incorrect) answers (ntp -na is the number of target problems for which the system fails to propose a solution), and nca be the number of correct answers (according to the generated function f) and the predicted answer. So, the precision prec is defined as the average of the ratios nca na , and the correct answer rate car is defined as the average of the ratios nca ntp .

The average is computed on 10 f for each of the 3 function generators. With the different sizes for CB + and CB -, 1872 cases are solved for each f.

Results and discussion

Table 3 presents the precision and correct answer rate of the five approaches for the differents function generators with various sizes of CB + and CB -. The results show that exploiting negative cases improves the CBR system results both when using inferences and not (comparison of AK + wrt AK +-and AK +I wrt AK +-I ).

Fig. 1 :

 1 Fig. 1: The generalization/specialization hierarchy of variations.

Table 1 :

 1 An example of formal context representing ingredients used in recipes.

Table 3 :

 3 AK + .53 .54 .54 .56 .56 .56 .56 .55 .55 .53 .54 .54 .56 .56 .56 .56 .55 .55 AK +-.53 .54 .61 .56 .77 .91 .56 .80 .93 .53 .53 .52 .56 .41 .34 .56 .30 .21 AK +I .49 .50 .50 .44 .44 .44 .42 .42 .43 .49 .50 .50 .44 .44 .44 .42 .42 .43 AK +-I .49 .52 .61 .44 .58 .72 .42 .68 .85 .49 .51 .56 .44 .53 .52 .42 .55 .51 prec and car for the three generators for different case base sizes.

	|CB + | =	16	32	48	16	32	48
	|CB -| = 0 8 16 0 16 32 0 24 48	0 8 16 0 16 32 0 24 48
	CNF N N	.82 .82 .82 .84 .84 .84 .84 .84 .84	.75 .75 .75 .84 .84 .84 .84 .84 .84
	AK + .81 .81 .80 .79 .79 .79 .78 .78 .79	.81 .81 .80 .79 .79 .79 .78 .78 .79
	AK +-.81 .85 .85 .79 .88 .91 .78 .90 .94	.81 .85 .85 .79 .88 .87 .78 .85 .83
	AK +I .78 .78 .78 .67 .67 .67 .76 .76 .76	.78 .78 .78 .67 .67 .67 .76 .76 .76
	AK +-I .78 .82 .84 .67 .84 .87 .76 .86 .92	.78 .82 .83 .67 .84 .86 .76 .86 .91
	DNF N N	.80 .80 .80 .82 .82 .82 .83 .83 .83	.74 .74 .74 .81 .82 .82 .83 .83 .83
	AK + .77 .77 .77 .76 .76 .76 .81 .81 .81	.77 .77 .77 .76 .76 .76 .81 .81 .81
	AK +-.77 .79 .83 .76 .85 .90 .81 .88 .94	.77 .79 .82 .76 .84 .82 .81 .85 .82
	AK +I .56 .56 .56 .66 .66 .66 .63 .63 .64	.56 .56 .56 .66 .66 .66 .63 .63 .64
	AK +-I .56 .72 .78 .66 .79 .87 .63 .85 .92	.56 .72 .77 .66 .79 .85 .63 .85 .91
	POL N N	.59 .59 .59 .63 .64 .64 .64 .64 .64	.54 .53 .54 .63 .63 .63 .64 .64 .64

Conclusion

*** todo ***


Dr Denis Frath

Dr Takeshi Sakano

Yohei Imaizumi

Dr Soichi Yokoyama

Prof Takashi K Hirose

Kenji Matsuda
email: kmatsuda@sbchem.kyoto-u.ac.jp

Matsuda

Diarylethene Self-Assembled Monolayers: Cocrystallization and Mixing-Induced Cooperativity Highlighted by Scanning Tunnelling Microscopy at the Liquid/Solid Interface

Keywords: Photochromism, Self-assembly, Scanning Tunneling Microscopy, Mixed Crystals, Induced Cooperativity

Stimulus control over 2-D multicomponent molecular ordering on surfaces is a key technology to realize advanced materials with stimuli-responsive surface properties. The 2-D molecular ordering formation along with photoisomerization was monitored by STM at octanoic acid/HOPG interface for the synthesized amide-containing diarylethene, which underwent photoisomerization between open-and closed-ring isomers and also side reaction to give annulated isomer. By the analysis of concentration dependence of surface coverage, the nucleation equilibrium constant (Kn) and the elongation equilibrium constant (Ke) were determined using cooperative model at the liquid/solid interface. It was found that the annulated isomer has very large equilibrium constant which explains the predominantly observed ordering of the annulated isomer. It was also found that the presence of the closed-ring isomer induces cooperativity in the formation of the molecular ordering of the open-ring isomer. The quantitative analysis of the ordering formation using cooperative model provided a new viewpoint toward 2-D multicomponent molecular ordering formation.

Introduction

Control over molecular nanostructure has become of first importance in a bottom-up strategy to elaborate functionalized surfaces for electronic devices. [1] In this context the study of the self-assembled monolayers (SAM) of organic building blocks on surfaces such as Au(111) or highly oriented pyrolytic graphite (HOPG) has been the subject of intense research. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Twodimensional (2-D) supramolecular self-assembly can be efficiently characterized by scanning tunneling microscopy (STM) at the liquid/solid interface with single-molecule resolution, [17] revealing influences of various factors such as concentration, [18][19][20] temperature, [20][21][22] electric pulse, [23][24][25] light, [25] or addition of guests. [26,27] In order to use light as an external trigger, a photoresponsive material is required. Among the organic photochromes, diarylethenes are very appealing due to the high thermal stability of both the open-and closed-ring isomers and their high fatigue resistance. [28][29][30] We have previously reported a light-induced switching between two different 2-D molecular orderings by isomerization of a diarylethene bearing pyrenyl group. [31] Herein we describe the properties of another diarylethene with three isomers (1o, 1c, and 1a, Fig. 1) that form stable 2-D molecular orderings on HOPG surface. A quantitative analysis of the cooperativity in the formation of their 2-D orderings and mixing of components in an ordering will be discussed based on concentration dependence of surface coverage for mono-and bi-component systems.

Results and Discussion

Synthesis and photophysical properties A diarylethene was designed to have long alkyl chains and amides group for stabilization of SAM on HOPG. [32] The openring isomer 1o was obtained by a two steps one-pot reaction starting from the corresponding bromo-substituted diarylethene with a yield of 94%. The closed-ring isomer 1c was prepared by a classic photoreaction carried out by UV light irradiation to a solution of 1o in ethyl acetate for 1 h. The isolated yield of compound 1c was 72%. A long-time irradiation (34 h) to a solution of 1o with UV light afforded the annulated isomer 1a with a 17% yield.

Absorption spectra were recorded for each isomer in octanoic acid (OA) since this solvent was used in STM measurements (Figure 2). The shape and magnitude of the absorption spectra were well reproduced by time-dependent density functional theory (TD-DFT) calculations at the B3LYP/6-311g(2d,p)//B3LYP/6-31g(d) level (See Figure S1-S5 in Supporting Information). The ratio of the photoreaction quantum yields of diarylethene 1 for the cyclization (Φo→c), cycloreversion (Φc→o), and annulation reactions (Φc→a) was estimated from the time evolution of absorption spectra upon UV irradiation (λirrad = 365 nm) in OA (Figure S6 in Supporting Information). Figure 3 shows the temporal change of concentration over irradiation time obtained by full-spectrum fitting of the time evolution of absorption spectra shown in Figure S6 in Supporting Information, using the spectra of the three isomers shown in Figure 2. The temporal differentiation of concentration of each isomer can be described by the reaction quantum yields (Φ) and molar absorption coefficients (ε) as follows:

where εo, εc, and εa are the molar absorption coefficients of each isomer at the irradiation wavelength, l is the optical path length, and I0 is the intensity of irradiation. To obtain a set of simulated curves of best fit, the ratio of three reaction quantum yields were optimized by non-linear regression analysis in every steps of which the simultaneous differential equations were numerically solved with experimentally determined initial parameters. The resulting ratio Φo→c:Φc→o:Φc→a was 1:0.047:0.001. The photoreaction quantum yield for the annulation reaction (Φc→a) was only 2.1% of the cycloreversion quantum yield (Φc→o). When Φo→c is assumed to be 0.59 as reported for a similar diarylethene derivative, [33] Φc→o and Φc→a become 2.8 × 10 -2 and 6.0 × 10 -4 , respectively.

Scanning Tunnelling Microscopy

As reported previously, compounds 1o, 1c, and 1a form characteristic stripe-patterned orderings (α, β, and γ, respectively) at the OA/HOPG interface (Figure 1). [32] It was also reported that only ordering γ, composed of compound 1a, was observed after irradiation with UV light on the surface, even if the annulated isomer is only a photochemical byproduct that is generated with the small photogeneration yield as mentioned above. [34] Ordering β, formed by the main photoproduct 1c, was not observed after irradiating the surface with UV light.

In order to rationalize the reason for the favorable appearance of ordering γ upon in situ UV irradiation, we investigated the concentration dependence of the surface coverage using STM (Figure 4). Compound 1o showed a gradual increase of the surface coverage as concentration in solution phase increases. The critical concentration, at which a saturated adsorption was observed, was around 30 µM for 1o. The closed-ring isomer 1c presented a brutal increase of the surface coverage at approximately the same critical concentration as the open-ring isomer (~30 µM). The annulated isomer 1a also showed a sharp increase of the surface coverage, and its critical concentration appeared at a lower concentration (~15 µM). An interesting feature of compound 1a is that the observed surface coverage was close to the theoretical maximum, meaning that almost all molecules available in solution are involved in the construction of ordering γ. This suggests a very high affinity of 1a for the HOPG surface.

Once saturated adsorption at the interface was reached, an increase in concentration resulted in the formation of aggregates and/or multilayers on the surface for each of the isomers (Figure S15, S24 and S31 in Supporting Information). At concentrations less than critical concentration, the domain size of ordered area on HOPG is usually larger than the scan size of STM (~200  200 nm 2 ). A part of a large domain was typically observed in some images, while no ordering was observed in the others. This fact brings about a large dispersion of surface coverage data and is inevitably associated with large error bars even if more data are collected (Figure 4). The stripepatterned orderings α, β, and γ were thermodynamically stable and no polymorph was observed in the range of concentrations used in this study.

Adsorption parameters (mono-component systems)

Although the critical concentrations for 1o and 1c are almost the same, the steepness of the concentration dependence is obviously different for the two isomers. Therefore, critical concentration alone is not sufficient to characterize the process of the ordering formation. Inspired by cooperative supramolecular polymerization in solution, [35,36] an equilibrium model at the liquid/solid interface has been recently developed by our group. [37] The model considers two different equilibrium constants, nucleation (Kn) and elongation constants (Ke), therefore it takes into account the intermolecular interactions between neighbouring molecules on the substrate. It is noted that the experimental concentration dependence of surface coverage was well reproduced by using the two parameters (Figure 4).

According to this model, the fractional coverage θ can be described as follows:

where σ is the degree of cooperativity defined as the ratio Kn/Ke, ct is the total concentration of the component, Asub is the total area of substrate, L is the volume of supernatant solution, S is the surface area occupied by one molecule, and NA is the Avogadro constant. Since molecular ordering formation at the liquid/solid interface is a process of 2-D crystal growth, it should comply with a cooperative model, in which Kn is smaller than Ke (σ < 1).

The simulated curves that fit the best with experimental data are shown in Figure 4 (solid lines) and the adsorption parameters are summarized in Table 1. Experimental data for the open-ring isomer 1o were sufficiently reproduced by considering isodesmic adsorption in which nucleation and subsequent elongation steps have identical equilibrium constant (Kn ~ Ke, σ ~ 1). The elongation constant of 1c (Ke = 6.6 × 10 4 M -1 ) is comparable to that of 1o (Ke = 6.8 × 10 4 M -1 ), whereas the nucleation constant of 1c (Kn = 6.6 × 10 -2 M -1 ) is almost six orders of magnitude less than that of the open-ring isomer 1o (Kn = 6.4 × 10 4 M -1 ). Thus, the steep rise in the concentration dependence for the closed-ring isomer 1c can be explained as a highly cooperative process (σ ≤ 10 -6 ). , the curves are no longer significantly dependent on σ. Therefore, σ less than 10 -6 cannot be determined precisely.

The cooperative simulation (Ke = 1.5 × 10 6 M -1 , σ ≤ 10 -6 ) gave the best-fitting curve for the experimental data of 1a, albeit the isodesmic simulation (Ke = 1.0 × 10 6 M -1 , σ = 1) also gave an acceptable fitting (Figure S8 in ESI). The result tells us that the simulated curves become less dependent on the degree of cooperativity (σ) when the surface coverage is close to the theoretical maximum. Thus it was difficult to determine which process controls the formation of ordering γ. Since no major difference was observed for 1a between isodesmic and cooperative curves, cooperative model was applied for the subsequent calculations.

The favourable appearance of ordering γ upon photoirradiation can be quantitatively explained by the large Ke value for 1a (Ke ≥ 10 6 M -1 ) that is associated with the very high affinity of the annulated isomer for the HOPG surface. The elongation constant for the annulated isomer 1a was even higher by almost two orders of magnitude (Ke ≥ 10 6 M -1 ) compared to 1o and 1c. Our model, using two adsorption parameters (Ke and σ), is a very convenient tool for quantitative evaluation of the concentration dependence of ordering formation on 2-D surface. Moreover, surface coverage θ can be calculated at any concentration based on the two parameters.

Pre-irradiation experiment

For a careful investigation of fractional surface coverage in a multi-component system composed of different isomers, concentration of each isomer in solution should be precisely determined. A solution of the open-ring isomer 1o (28.7 μM) was irradiated with UV light (λirrad = 365 nm) for 5, 15, and 45 minutes and the concentrations of each sample were determined by UVvis. spectroscopy. STM images were then acquired for the concentration-determined three samples that were irradiated before the deposition on HOPG (Figure 5). Respective fractional coverage observed for orderings α, β, and γ are summarized in Table S1 in Supporting Information. 4).

From the exact composition of the mixture, the fractional coverage θ for each isomer can be calculated based on the adsorption parameters determined above. The experimental fractional coverage of ordering γ (θγ,exp = 0, 0.32, and 0.79 for the samples after UV irradiation for 3, 15, and 45 min, respectively) was quite similar to the simulated values (θγ,sim = 0.09, 0.26, and 0.87), suggesting that the adsorption of 1a can be reproduced with mono-component parameters. However, experimental coverage for 1o and 1c (θα,exp = 0 for all samples; θβ,exp = 0.35, 0.18, and 0.005) were surprisingly different from the expectations (θα,sim = 0.40, 0.32, and 0.21; θβ,sim = 0.08, 0.02, and 0); the experimental coverage for ordering β was significantly higher than the predictions and ordering α was not observed in the experiment. These observations suggested that the open-and closed-ring isomers significantly influence each other during the formation of their 2-D orderings. As described in the next section, the experimental surface coverage was reproduced well by considering a mixing of the two isomers in the orderings α and β.

Adsorption parameters (bi-component systems)

In order to reveal the interaction between the two isomers 1o and 1c, concentration dependence of the surface coverage for the bi-component system was carefully investigated (Figure 6). Interestingly, only ordering β was observed for the ratios (1o/1c) of 0/100, 37/63, and 51/49 (Figure 6a), and ordering α was solely observed for 78/22 and 100/0 (Figure 6b). Both orderings α and β were observed simultaneously in a STM image for a narrow range of ratios such as 62/38. 32 The simultaneous observation of the two orderings is also possible by drop-casting a concentrated solution of 1c to a pre-adsorbed solution of 1o. [32] The effect of the presence of 1o on the formation of ordering β is clearly seen in Figure 6a, where we assumed that the ordering β consists of only the closed-ring isomer and surface coverage of ordering β is plotted against the concentration of 1c. If the formation of ordering β is independent of the presence of the open-ring isomer 1o, the same concentration dependence is expected for any ratio of isomers (1o/1c). However, the critical concentration of 1c was obviously reduced from 26 to 21 µM with increasing the fraction of 1o. At a given concentration of 1c, the surface coverage of ordering β is significantly increased by addition of 1o. For instance, pure 1c at 15 µM does not form any ordering. For the samples with the ratio of 37/63 and 51/49 containing 15 µM of 1c, surface coverage of ordering β reaches 25% and 56%, respectively. This significant increase of surface coverage upon addition of 1o suggests that the ordering β is likely a mixed crystal composed of the two isomers. S2 in Supporting Information.

Since the mixing of two isomers in orderings α and β was experimentally suggested, we assumed that the open-and closed-ring isomers cocrystalize on the 2-D surface and that both 1o and 1c contribute equally to the formation of orderings α and β. The surface coverage shown in Fig. 6 was plotted against the total concentration of the two isomers [1o + 1c]. The resulting curves are shown in Figure 7 and the corresponding adsorption parameters are summarized in Table 2.

Upon mixing the open-ring isomer 1o to the ordering β that is mainly consisting of the closed-ring isomer 1c, critical concentration increased from 26 µM to ~40 µM for the ratio 1o/1c of 51/49 (Figure 7a). This is associated with the decrease of the elongation equilibrium constant (Ke) from 6.6 × 10 4 to 3.9 × 10 4 M -1 in the adsorption parameter (Table 2). The decrease of Ke is maybe because of a thermodynamic destabilization of ordering β by the incorporation of the open-ring isomer 1o, which has a slightly different conformation to 1c. Upon mixing of 1o to ordering β, significant decrease of cooperativity (i.e., increase of σ from less than 10 -6 to 4.9 × 10 -3 ) was also observed, which originates from the increase of the nucleation equilibrium constant (Kn) (from 6.6 × 10 -2 to 1.9 × 10 2 M -1 ). Because the open-ring isomer 1o has a higher nucleation value for the formation of ordering α (Kn = 6.4 × 10 4 M -1 ), it would act as a seeding agent giving a nucleation point for subsequent elongation of ordering β.

Upon mixing the closed-ring isomer 1c to ordering α that is mainly composed of the open-ring isomer 1o, a steep rise emerged in the concentration dependence of surface coverage (Figure 7b). In the adsorption parameters, the prominent increase of the cooperativity (i.e., σ decreased from 0.95 to 6.0 × 10 -4 ) was observed (Table 2), which has already been mentioned on the analysis based only on concentration [1o]. Thus, mixing-induced cooperativity in the formation of ordering α was also supported by the analysis of the total concentration [1o + 1c].

The experimental surface coverage for the pre-irradiation experiment, shown in Figure 5, was reanalyzed by considering the mixing of the open-and the closed-ring isomers in the ordering α and β. In this analysis, the adsorption parameters for the ratio 37/63 (Ke = 4.4  10 4 M -1 , σ = 5.2  10 -4 ) were adopted since the experimental ratio is close to this value (i.e., 1o/1c = (35.4 ± 1.3)/(64.6 ± 1.3) for the samples irradiated for 5, 15, and 45 min). As shown in Table 3, the experimental surface coverage was successfully reproduced by the simulation. In this context, the cocrystallization of the open-and the closed ring isomers into ordering β is further supported by the simulation considering the total concentration [1o + 1c]. 2).

f Values obtained assuming Ke = 0 since no ordering was experimentally observed in the condition of the ratio of the two isomers 1o/1c. ).

FULL PAPER

Although we carefully investigated high-resolution STM images of the cocrystallized orderings, no significant difference has been observed at this time between ordering α obtained from a pure solution of 1o (Figure 8a) and from a mixed solution 1o/1c (Figure 8b). It was the same for ordering β obtained from a pure solution of 1c (Figure 8c) and from a mixed solution 1o/1c (Figure 8d). Owing to a rapid exchange of components during adsorption/desorption equilibrium at the OA/HOPG interface, clear distinction of the two isomers at single-molecule resolution may be difficult under ambient conditions.

Real-time in-situ irradiation

Next, photochemical interchanges between orderings upon insitu photoirradiation were directly monitored by a real-time STM scanning (Figure 9). Contrary to our expectation, the observed interchanges between orderings were different from that observed from the pre-irradiation experiment shown in Figure 5. STM images were continuously scanned at almost the same position on the substrate for 2 h (cf. cross mark on Figure 9). After observation of the first STM image of the open-ring isomer 1o (t = 0 min), the surface was constantly irradiated with UV light (365 nm) without stopping STM scans. In the initial image, several domains of ordering α were observed. Upon UV irradiation, the surface coverage of ordering α was gradually decreased (12 min) until it was completely disappeared (59 min). In the meantime, several small domains of ordering γ, composed of the annulated isomer 1a, appeared (14 min). These domains enlarged like a crystal growth (28 min) and eventually covered the substrate almost dominantly (38 min -1 h 21 min). According to the simulated evolution of concentrations (Figure 3 and S7 in Supporting Information), the closed-ring isomer 1c was expected to be predominant in the early stage of the irradiation. However, ordering  was never observed during the course of the in-situ irradiation. The favourable appearance of ordering γ upon UV irradiation on the surface is consistent with the previously reported result. [32] In the pre-irradiation experiment (Figure 5), the isomers with different ratios of 1o/1c can start to adsorb on an empty surface. On the other hand, in the in-situ irradiation experiment (Figure 9), the surface is already almost fully occupied by ordering α. We suppose that the closed-ring isomer 1c, produced during the in-situ irradiation, was progressively included in the pre-organized ordering α. Therefore, the kinetically metastable ordering α, composed of the two isomers 1o and 1c, was constantly observed until it was replaced by the more stable ordering γ having higher affinity for the HOPG surface.

Conclusions

In this work, concentration dependence of surface coverage and photochemical interchanges between molecular orderings for the three isomers of a diarylethene were carefully investigated by UV-vis. spectroscopy and STM measurements. Adsorption parameters were determined using a cooperative equilibrium model on 2-D surface for pure 1o, 1c and 1a. According to these mono-component parameters, the open-ring isomer 1o showed an isodesmic process (σ ~ 1) whereas the closed-ring isomer 1c showed a highly cooperative process (σ ≤ 10 -6 ). The annulated isomer 1a showed a very high affinity for HOPG surface (Ke ≥ 10 6 ). Careful inspections on the bi-component system of 1o and 1c suggested that the two isomers influence each other during the formation of molecular orderings and form mixed crystals. Moreover, mixing-induced cooperativity in ordering formation process was observed by the STM measurements: the closedring isomer 1c can induce cooperativity in the formation of ordering α that is mainly composed of the open-ring isomer 1o. The results presented in this work provide a better understanding of mixing of components in a molecular ordering and photoinduced interchanges between orderings occurring at the liquid/solid interface.

Experimental Section

General Methods. Reagents and solvents were obtained from commercial suppliers and used without further purification. 1,2-bis(2methyl-5-bromothiophene-3-yl)hexafluorocyclopentene and N-hexadecyl-4-iodobenzamide were prepared according to methods reported in the literature. [32,38] All reactions were monitored by thin-layer chromatography carried out on 0.2 mm Merck silica gel plates (60F-254). Column chromatography was performed on silica gel (Nakarai Tesque, 70-230 mesh). 1 H and 13 C NMR spectra were recorded on a JEOL JNM-ALPHA500 or JNM-ECA600 instruments. Proton chemical shifts are reported in ppm downfield from tetramethylsilane (TMS). Carbon chemical shifts are reported in ppm by reference to solvent signal. Mass spectra were obtained by a Thermo Scientific Exactive mass spectrometer ESI-Orbitrap.

Synthesis of the open-ring isomer 1o.

To a solution of 1,2-bis(2methyl-5-bromo-3-thienyl)hexafluorocyclopentene (200 mg, 0.380 mmol) in dry THF (15 mL) at -78 °C, under nitrogen atmosphere, was added n-BuLi (1.6 M in hexane, 0.60 ml, 0.96 mmol). The resulting mixture was stirred for 1 h at -78 °C. Then tributyl borate (0.30 mL, 1.1 mmol), was added. The solution was warmed up to room temperature and stirred for 3 h. Then N-hexadecyl-4-iodobenzamide (358 mg, 0.759 mmol) and aq. K2CO3 (20 wt %, 15 mL) were added. After Argon was bubbled through the solution, Pd(PPh3)4 was added and the solution was refluxed for 16 h under Argon atmosphere. After cooling down it was washed with aq. NH4Cl and extracted with diethyl ether. Organic layers were collected, dried over MgSO4, filtrated and concentrated under vacuum. Purified by silica gel chromatography eluted with chloroform. A white-blue powder. Yield : 94% (378 mg). 1 (m,4H), 1.39-1.24 (m, 52H), 0.88 (t, J = 7.0 Hz, 6H); 13 C NMR: Not obtained due to the limited amount of compound; UV-Vis (Octanoic Acid) λmax, nm (ε, M -1 cm -1 ): 560 (9 100), 313 (29 100); HR-ESI-MS (m/z) [M + H] + calcd for C61H84F6N2O2S2H + , 1055.5951; found: 1055.5936.

Theoretical calculations. The geometrical optimization was carried out at the RB3LYP/6-31g(d) level of theory. Convergence at a local minimum structure was confirmed by no imaginary frequencies on frequency analysis. Successively the optimized local minimum structures were subjected to TD-DFT calculations to obtain 10 excited states from the lowest energy transition at the identical level of theory.

UV-vis. Spectroscopy and Photochemical Reactions. Absorption spectra were measured on a spectrophotometer (HITACHI U-3310). Optical length of the quartz cells were 1 cm. Photoirradiation experiments on HOPG surface were performed by a Keyence UV-400 UV-LED equipped with an optical fiber (0.30 W/cm 2 , λ = 365 nm) or a USHIO 500W Xe lamp with a sharp cut filter (UV-29) and bandpass filter (U340) for UV light (0.64 W/cm 2 , λmax = 313 nm), and with sharp cut filters (U-29 and Y-48) for visible light (0.32 W/cm 2 , λ > 460 nm).

Scanning Tunneling Microscopy. All STM experiments were performed at room temperature and ambient conditions. The STM images were acquired with an Agilent technologies 5500 scanning probe microscope in the constant current mode. The STM tips were mechanically cut from a Pt/Ir (80/20, diameter 0.25 mm) wire. Highly Oriented Pyrolytic Graphite (HOPG) (purchased from the Bruker Co.) was used as substrate. The concentrations of solutions were controlled by UV-vis. A drop of the solution (8 μL) was deposited onto freshly cleaved HOPG, the tip was immersed into the solution and images were scanned. Topography images were obtained using the software WSxM. [39]

Entry for the Table of Contents

FULL PAPER

Let's be cooperative! Adsorption process at the octanoic acid/highly oriented pyrolytic graphite interface was investigated for three isomers of a diarylethene derivative. The formation of mixed crystals on 2-D surface and "mixing-induced cooperativity" were highlighted thanks to a cooperative model. Thus a better understanding of photochemical interchanges at the interface became possible.

Figure 1 .

 1 Figure 1. Chemical structures and STM images of (a) the open-ring isomer 1o (ordering α), (b) the closed-ring isomer 1c (ordering β), and (c) the annulated isomer 1a (ordering γ). See ref 32 for details of the orderings.

Figure 2 .

 2 Figure 2. Absorption spectra of compounds 1o (black), 1c (blue), and 1a (pink) in octanoic acid and theoretical oscillator strengths calculated by TD-DFT.

Figure 3 .

 3 Figure 3. Evolution of the composition of the three isomers in octanoic acid upon UV irradiation (λirrad = 365 nm, [1o]t=0 = 29.4 µM, V = 3.0 mL, l = 1 cm).

Figure 4 .

 4 Figure 4. Concentration dependence of the surface coverage of 1o (black), 1c (blue), and 1a (pink) at the OA/HOPG interface. See Supporting Information for details of observed STM images at different concentration.

Figure 5 .

 5 Figure 5. Representative STM images (200 x 200 nm²) obtained by deposition of pre-irradiated solutions in OA (Iset = 10 pA, Vbias = -1.0 V, [1o]t=0 = 28.7 M). UV irradiation (λirrad = 365 nm) was conducted for (a) 5, (b) 15, and (c) 45 min prior to the deposition on HOPG. Concentration of each sample were precisely determined by UV-vis. spectroscopy (Table4).

Figure 6 .

 6 Figure 6. Concentration dependence of the surface coverage of (a) ordering  for 1c and mixtures of 1o/1c (37/63 and 51/49), and that of (b) ordering  for 1o and a mixture of 1o/1c (78/22). Simulated curves (solid lines) were obtained with the adsorption parameters summarized in TableS2in Supporting Information.

Figure 7 .

 7 Figure 7. Concentration dependence of the surface coverage of (a) ordering  for 1c and mixtures of 1o/1c (37/63 and 51/49), and (b) that of ordering  for 1o and a mixture of 1o/1c (78/22) against total concentration of the two isomers [1o + 1c].

a

  simulated by the cooperative model on 2-D surface

Fig. 5 .b

 5 Time of irradiation with UV light (λirrad = 365 nm).c Concentration of samples was determined by UV-vis. spectroscopy before the deposition on HOPG surface. d Experimental fractional surface coverage observed by STM measurements. e Simulated by the cooperative model using the adsorption parameters based on the total concentration of the two isomers [1o + 1c] (see Table

gh

  Values obtained using bi-component parameters (Ke = 4.4Values obtained using mono-component parameters (Ke = 1.5

Figure 8 .

 8 Figure 8. High-resolution STM images (50 x 50 nm², Iset = 10 pA, Vbias = -1.0 V) of (a) ordering α for pure 1o ([1o] = 16.9 M) and (b) for the sample with 1o/1c = 78/22 ([1o + 1c] = 16.1 M) (c) That of ordering β for pure 1c ([1c] = 24 M) and (d) for the sample with 1o/1c = 37/63 ([1o + 1c] = 27 M).

Figure 9 .

 9 Figure 9. STM images (200 x 200 nm²) of the in-situ photoirradiation of 1o at the OA/HOPG interface (Iset = 10 pA, Vbias = -1.0 V, [1o]t=0 ~30 M).

  Denis Frath, Takeshi Sakano, Yohei Imaizumi, Soichi Yokoyama, Takashi Hirose, and Kenji Matsuda* Page No. -Page No. Diarylethene Self-Assembled Monolayers: Cocrystallization and "Mixing-Induced Cooperativity" Highlighted by Scanning Tunneling Microscopy at the Liquid/Solid Interface

Table 1

 1 Adsorption parameters of 1o, 1c, and 1a on HOPG surface

	a

a simulated by the cooperative model on 2-D surface (mono-component systems) b for values below 10 -6

Table 2

 2 Best-fitting adsorption parameters for 1o/1c solutions considering [1o + 1c] (bi-component parameters)

			a
	Ratio1o/1c	0/100	37/63	51/49		78/22	100/0
	Ordering Ke (M -1 ) Kn (M -1 )	β 6.6 × 10 4 6.6 × 10 -2	β 4.4 × 10 4 2.3 × 10 1	β 3.9 × 10 1.9 × 10	4	α 7.2 × 10 4	α 6.8 × 10 4

Table 3

 3 Experimental surface coverage for the pre-irradiation experiment and simulated values considering a mixing of 1o and 1c in the ordering α and β

	b	[1o] (μM)	[1c] (μM)	[1a] (μM)	1o/1c	θα,exp	θβ,exp	θγ,exp	θα,sim	f	θβ,sim	g	θγ,sim	h
	5	9.4	16.1	1.8	37/63	0	0.35	0	0		0.31	0.09
	15	7.8	14.9	3.9	34/66	0	0.18	0.32	0		0.14	0.26
	45	5.1	9.5	11.3	35/65	0	0.005	0.79	0		0.003	0.87

a Concentration c Surface coverage (experimental data) d Surface coverage (simulated) e Time (min) a Corresponding STM images are shown in

  .52, 136.54, 135.72, 127.59, 127.22, 115.27, 66.35, 40.51, 32.15, 29.92, 29.88, 29.82, 29.77, 29.59, 29.54, 27.24, 25.47, 22.91, 14.34; UV-vis (Octanoic Acid) λmax, nm (ε, M -1 cm -1 ): 598 (19 700), 390 (12 000), 377 (12 000), 320 (34 500); HR-ESI-MS (m/z) [M + H] + calcd for C61H84F6N2O2S2H + , 1055.5951; found: 1055.5940.

	H NMR (500 MHz, CDCl3) δ (ppm): 7.71 (d, J = 8.6 Hz, 2H), 7.58 (d, J = 8.6 Hz, 2H), 7.34 (s, 2H), 6.13-6.10 (m, 2H), 3.49-3.44 (m, 4H), 1.99 (s, 6H), 1.64-1.61 (m, 4H), 1.40-1.26 (m, 52H), 0.88 (t, J = 7.0 Hz, 6H); 13 C NMR (151 MHz, CDCl3) δ (ppm): 166.90, 142.53, 141.31, 136.17, 134.14, 127.88, 126.23, 125.65, 123.60, 40.42, 32.13, 29.89, 29.86, 29.80, 29.77, 29.57, 29.55, 27.24, 22.89, 14.83, 14.32; UV-vis (Octanoic Acid) λmax, nm (ε, M -1 cm -1 ): 311 (46 900); HR-ESI-MS (m/z) [M + H] + calcd for C61H84F6N2O2S2H + , 1055.5951; found: 1055.5948. Synthesis of the closed-ring isomer 1c. A solution of 1o (20 mg) in ethyl acetate (200 mL) was irradiated with a UV light (λ = 313 nm) for 1 h. Compound 1c was purified by HPLC (Mightysil Si60 250-20, eluted with dichloromethane/EtOAc 90/10, 5.0 mL/min, retention time 19 min). A blue solid. Yield 72% (14.4 mg). 1 H NMR (500 MHz, CDCl3) δ (ppm): 7.80 (d, J = 8.6 Hz, 4H), 7.61 (d, J = 8.6 Hz, 4H), 6.73 (s, 2H), 6.20-6.16 (m, 2H), 3.49-3.45 (m, 4H), 2.20 (s, 6H), 1.68-1.61 (m, 4H), 1.39-1.26 (m, 52H), 0.88 (t, J = 7.0 Hz, 6H); 13 C NMR (151 MHz, CDCl3) δ (ppm): 166.50, 156.95, 149Synthesis of the annulated isomer 1a. A solution of 1o (20 mg) in ethyl acetate (200 mL) was irradiated with UV light (λ = 313 and 365 nm) for 34 h (2 × 17 h). Then it was irradiated with visible light (λ > 480 nm) for 17 h. A first purification by HPLC (Mightysil Si60 250-20, eluted with dichloromethane/EtOAc 90/10, 5.0 mL/min, retention time 12 min) was used to remove the largest part of undesired isomers. Another irradiation sequence with visible light (λ > 480 nm) was performed for 17 h. Compound 1a was purified by HPLC (Mightysil Si60 250-20, eluted with dichloromethane/EtOAc 90/10, 5.0 mL/min, retention time 19.5 min). A deep purple solid. Yield 17% (3.4 mg). 1 H NMR (500 MHz, CDCl3) δ (ppm): 7.76 (d, J = 8.6 Hz, 2H), 7.59 (d, J = 8.6 Hz, 2H), 6.57 (s, 2H), 6.10-6.07 (m, 2H), 3.47-3.44 (m, 4H), 2.80 (s, 3H), 2.77 (s, 3H) 1.64-1.60

Acknowledgements

This work was supported by NEXT program (No. GR062), a Grant-in-Aid for Scientific Research on Innovative Areas "photosynergetics" (No. 26107008) from the MEXT, Grant-in-Aid for Young Scientists (B) (No. 25810048) and a Grant-in-Aid for JSPS Fellows (No. 2604341) from the Japan Society for the Promotion of Science (JSPS). D.F. acknowledges the JSPS for a postdoctoral fellowship.


Denis Frath

Soichi Yokoyama

Takashi Hirose

Kenji Matsuda
email: kmatsuda@sbchem.kyoto-u.ac.jp

Photoresponsive supramolecular self-assemblies at the liquid/solid interface

Keywords: photochromism, scanning tunneling microscopy, self-assembly, cooperative effects

Introduction

Surface-adsorbed molecular layers can be constructed by self-assembly. Scanning tunneling microscopy (STM), which was developed by Binnig, Roher, and co-workers, provides useful insights into the structure, properties, and dynamics of the assembly with submolecular resolution [START_REF] Binning | Surface studies by scanning tunneling microscopy[END_REF]. STM measurements can be performed on metal surfaces under ultra-high vacuum conditions, at the solid/gas interface, or at the liquid/solid interface. In assemblies formed at the liquid/solid interface, molecules are constantly exchanged between the substrate interface and the supernatant solution phase. Therefore, STM measurements at the liquid/solid interface, which were first developed by Rabe and co-workers, can provide information on the process of two-dimensional (2D) self-assembly, or in other words, 2D crystallization [START_REF] Rabe | Commensurability and mobility in two-dimensional molecular patterns on graphite[END_REF]. Thus, supramolecular chemistry at the liquid/solid interface has been extensively studied by using STM. The main fields of interest are chirality, polymorphism, guest inclusion, as well as responsiveness to stimuli, such as light, electric fields/pulses, and temperature . In particular, the photochemical control of the assembly of structures at liquid/solid interfaces has recently attracted interest. In this review, we will provide an overview of photochemically controlled surface-adsorbed molecular layers that have been studied using STM, focusing on photoresponsive supramolecular self-assemblies at the liquid/solid interface.

Photochemical modification of molecular assemblies studied by STM

Light is a typical stimulus that can be used in a non-invasive manner, without requiring additives that could disturb the system. The photochemical reaction of the molecules constituting the assembly can manipulate the whole assembly. By controlling the wavelength and polarization of the irradiation light, it is possible to selectively excite specific molecules. In particular, the use of photochromic compounds, which undergo reversible isomerization, enables reversible control of the assembly. Photoswitching of the properties of photochromic molecules or molecular assemblies has attracted great interest [START_REF]Molecular Switches[END_REF][START_REF]Photon-Working Switches[END_REF][START_REF] Russew | Photoswitches: from molecules to materials[END_REF][START_REF] Irie | Photochromism of diarylethene molecules and crystals: memories, switches, and actuators[END_REF].

The photopolymerization of diacetylene on surfaces has been studied extensively since the 1990s [START_REF] Grim | Submolecularly resolved polymerization of diacetylene molecules on the graphite surface observed with scanning thnneling microscopy[END_REF][START_REF] Miura | Light-and STM-tip-induced formation of one-dimensional and two-dimensional organic nanostructures[END_REF][START_REF] Xue | Patterned monolayer self-assembly programmed by side chain shape: four-component gratings[END_REF][START_REF] Yang | Shape-directed patterning and surface reaction of tetra-diacetylene monolayers: formation of linear and two-dimensional grid polydiacetylene alternating copolymers[END_REF][START_REF] Guo | Two-dimensional self-assembly of diacetylenic acid derivatives and their light-induced polymerization on HOPG surfaces[END_REF]. De Schryver and co-workers reported the photopolymerization of diacetylene molecules assembled at the undecanol/HOPG interface [START_REF] Grim | Submolecularly resolved polymerization of diacetylene molecules on the graphite surface observed with scanning thnneling microscopy[END_REF]. The molecular packing at the interface was favorable for the photopolymerization of diacetylene. Recently, Zimmt and co-workers reported the polymerization reaction of tetra-diacetylenes with careful control of the molecular packing at the phenyloctane/HOPG interface [START_REF] Yang | Shape-directed patterning and surface reaction of tetra-diacetylene monolayers: formation of linear and two-dimensional grid polydiacetylene alternating copolymers[END_REF]. It is also worth mentioning that tip-induced polymerization of diacetylenes using STM was reported by Aono and co-workers [START_REF] Okawa | Nanoscale control of chain polymerization[END_REF][START_REF] Okawa | Linear chain polymerization initiated by a scanning tunneling microscope tip at designated positions[END_REF][START_REF] Okawa | Chemical wiring and soldering toward all-molecule electronic circuitry[END_REF].

The photoresponse of photochromic molecules has been studied under ultra-high vacuum conditions [START_REF] Henzl | Reversible cis-trans isomerization of a single azobenzene molecule[END_REF][START_REF] Henzl | Irreversible isomerization of the azobenzene derivate methyl orange on Au(111)[END_REF][START_REF] Alemani | Electric field-induced isomerization of azobenzene by STM[END_REF][START_REF] Comstock | Reversible photomechanical switching of individual engineered molecules at a metallic surface[END_REF][START_REF] Dri | Spatial periodicity in molecular switching[END_REF][START_REF] Pechenezhskiy | Self-assembly and photomechanical switching of an azobenzene derivative on GaAs(110): scanning tunneling microscopy study[END_REF][START_REF] Böckmann | Direct observation of photoinduced tautomerization in single molecules at a metal surface[END_REF]. The group of Hecht and Grill and the group of Crommie reported the switching of individual molecules of azobenzene derivatives [START_REF] Alemani | Electric field-induced isomerization of azobenzene by STM[END_REF][START_REF] Comstock | Reversible photomechanical switching of individual engineered molecules at a metallic surface[END_REF][START_REF] Dri | Spatial periodicity in molecular switching[END_REF]. Moreover, Hecht, Grill, and co-workers reported the switching behavior of (4-methoxy-3,3ʹ,5,5ʹ-tetra-tert-butylazobenzene) on Au(111) under ultra-high vacuum conditions. The formation of a periodic pattern of cis isomers was observed after applying a voltage pulse (Fig. 1) [START_REF] Dri | Spatial periodicity in molecular switching[END_REF]. Several groups have reported the observation of different appearance in the STM image for the different isomers of photochromic compounds [START_REF] Umemoto | Photoisomerization observed by means of scanning tunneling microscopy[END_REF][START_REF] Oreshkin | Direct STM observation of electronic structure modification of naphthacenequinone molecules due to photoisomerization[END_REF][START_REF] Yasuda | Phase switching of a single isomeric molecule and associated characteristic rectification[END_REF][START_REF] Katsonis | Reversible conductance switching of single diarylethenes on a gold surface[END_REF][START_REF] Xu | STM investigation of the photoisomerization of an azobis-(benzo-15-crown-5) molecule and its self-assembly on Au(111)[END_REF][START_REF] Otsuki | STM observation of labile axial ligands to zinc porphyrin at liquid/solid interface[END_REF][START_REF] Pace | Cooperative light-induced molecular movements of highly ordered azobenzene self-assembled monolayers[END_REF][START_REF] Mativetsky | Azobenzenes as light-controlled molecular electronic switches in nanoscale metal-molecule-metal junctions[END_REF][START_REF] Kumar | Reversible photo-switching of single azobenzene molecules in controlled nanoscale environments[END_REF][START_REF] Elbing | Single component self-assembled monolayers of aromatic azobiphenyl: influence of the packing tightness on the sam structure and light-induced molecular movements[END_REF][START_REF] Arramel | Reversible light induced conductance switching of asymmetric diarylethenes on gold: surface and electronic studies[END_REF][START_REF] Snegir | STM observation of open-and closed-ring forms of functionalized diarylethene molecules self-assembled on a Au(111) surface[END_REF][START_REF] Snegir | Switching at the nanoscale: light-and STM-tip-induced switch of a thiolated diarylethene self-assembly on Au(111)[END_REF]. The apparent height in the STM image provides information on both molecular length and conductance; therefore, data regarding the photoswitching of molecular conductance can be obtained. Conductivity characteristics have also been investigated by the measurement of I-V curves. Feringa and co-workers reported the observation of photoswitching in STM images associated with the photochromic reaction of a diarylethene molecule. The closed-ring isomer of diarylethene was demonstrated to have higher conductance than the open-ring isomer [START_REF] Katsonis | Reversible conductance switching of single diarylethenes on a gold surface[END_REF][START_REF] Arramel | Reversible light induced conductance switching of asymmetric diarylethenes on gold: surface and electronic studies[END_REF].

Samorì and co-workers reported surface modification using photoresponsive azobenzene [START_REF] Pace | Cooperative light-induced molecular movements of highly ordered azobenzene self-assembled monolayers[END_REF][START_REF] Mativetsky | Azobenzenes as light-controlled molecular electronic switches in nanoscale metal-molecule-metal junctions[END_REF][START_REF] Elbing | Single component self-assembled monolayers of aromatic azobiphenyl: influence of the packing tightness on the sam structure and light-induced molecular movements[END_REF]. The molecules of the azobenzene derivative 4ʹ-(biphenyl-4-ylazo)-biphenyl-4-thiol were grafted on a Au surface, and its photochemical response was studied [START_REF] Pace | Cooperative light-induced molecular movements of highly ordered azobenzene self-assembled monolayers[END_REF]. Switching of the entire 2D crystal domain was observed, suggesting a cooperative process (Fig. 2). Additionally, not only light-induced switching, but also tip-induced switching, is possible. The tip-induced switching of thiolated diarylethene assembled on a Au(111) surface was reported by Snegir and co-workers [START_REF] Snegir | STM observation of open-and closed-ring forms of functionalized diarylethene molecules self-assembled on a Au(111) surface[END_REF][START_REF] Snegir | Switching at the nanoscale: light-and STM-tip-induced switch of a thiolated diarylethene self-assembly on Au(111)[END_REF]. In systems under ultra-high vacuum and at air/solid interfaces, the molecules are immobilized on the surface, and therefore the stability of these materials is high. On the other hand, in the case of liquid/solid interfaces, molecules are exchanged between the substrate interface and the supernatant solution phase. Therefore, STM at the liquid/solid interface provides a suitable platform to investigate their 2D self-assembly processes.

Supramolecular control of molecular assemblies formed at the liquid/solid interface

Among several platforms for measuring STM, liquid/solid interface is particularly interesting because exchange occurs between the molecules at the interface and in solution.

Therefore, the 2D self-assembly process can be studied quantitatively from a supramolecular chemistry perspective [START_REF] Rohde | From a lamellar to hexagonal self-assembly of bis(4,4′-(m,m′-di(dodecyloxy)phenyl)-2,2′-difluoro-1,3,2-dioxaborin) molecules: a trans-to-cis-isomerization-induced structural transition studied with STM[END_REF][START_REF] Florio | Frustrated ostwald ripening in self-assembled monolayers of cruciform π-systems[END_REF][START_REF] Furukawa | Structural transformation of a two-dimensional molecular network in response to selective guest inclusion[END_REF][START_REF] Lei | One building block, two different supramolecular surface-confined patterns: concentration in control at the solid-liquid interface[END_REF][START_REF] Katsonis | Locking of helicity and shape complementarity in diarylethene dimers on graphite[END_REF][START_REF] Blunt | Directing two-dimensional molecular crystallization using guest templates[END_REF][START_REF] Ilan | Scanning tunneling microscopy images of alkane derivatives on graphite: role of electronic effects[END_REF][START_REF] Gutzler | Reversible phase transitions in self-assembled monolayers at the liquid-solid interface: temperature-controlled opening and closing of nanopores[END_REF][START_REF] Zhao | Molecule length directed self-assembly behavior of tetratopic oligomeric phenylene-ethynylenes end-capped with carboxylic groups by scanning tunneling microscopy[END_REF][START_REF] Tahara | Control and induction of surface-confined homochiral porous molecular networks[END_REF][START_REF] Friesen | Single molecule imaging of oxygenation of cobalt octaethylporphyrin at the solution/solid interface: thermodynamics from microscopy[END_REF][START_REF] Ciesielski | Concentration-dependent supramolecular engineering of hydrogen-bonded nanostructures at surfaces: predicting self-assembly in 2D[END_REF][START_REF] Blunt | Temperature-induced structural phase transitions in a two-dimensional self-assembled network[END_REF][START_REF] Zheng | Bilayer molecular assembly at a solid/liquid interface as triggered by a mild electric field[END_REF][START_REF] Ciesielski | Dynamic covalent chemistry of bisimines at the solid/liquid interface monitored by scanning tunnelling microscopy[END_REF][START_REF] Bhattarai | A single molecule level study of the temperature-dependent kinetics for the formation of metal porphyrin monolayers on Au(111) from solution[END_REF][START_REF] Li | Tip-induced chemical manipulation of metal porphyrins at a liquid/solid interface[END_REF][START_REF] Greenwood | Covalent modification of graphene and graphite using diazonium chemistry: tunable grafting and nanomanipulation[END_REF][START_REF] Cometto | Local conformational switching of supramolecular networks at the solid/liquid interface[END_REF][START_REF] Fang | Dynamic control over supramolecular handedness by selecting chiral induction pathways at the solution-solid interface[END_REF]. Molecular assemblies at the liquid/solid interface have been studied in terms of chirality, polymorphism, guest inclusion, etc.

Responses to various stimuli, including not only light, but also electric fields/pulses, temperature, etc., have also been studied at the liquid/solid interface. The reorganization induced by an external stimulus can lead to dramatic changes in the adsorbed monolayer.

Tobe, De Feyter, Tahara, and co-workers demonstrated that the 2D chiral honeycomb arrangement of alkoxylated dehydrobenzo [START_REF] Bonifazi | Supramolecular chemistry at interfaces: molecular recognition on nanopatterned porous surfaces[END_REF]annulene derivatives can be controlled by molecular recognition and thermodynamic control. Chiral induction by dehydrobenzoannulene with a chiral side chain was demonstrated [START_REF] Tahara | Control and induction of surface-confined homochiral porous molecular networks[END_REF]. Moreover, careful investigation of the assembly process revealed the effects of temperature and concentration in inducing the reversal of the chirality upon heating [START_REF] Fang | Dynamic control over supramolecular handedness by selecting chiral induction pathways at the solution-solid interface[END_REF].

Wan and co-workers reported that the structure of an assembly of bis(4,4ʹ-(m,mʹ-di(dodecyloxy)phenyl)-2,2ʹ-difluoro-1,3,2-dioxaborine) was converted from lamellar to hexagonal by the thermal-annealing process [START_REF] Rohde | From a lamellar to hexagonal self-assembly of bis(4,4′-(m,m′-di(dodecyloxy)phenyl)-2,2′-difluoro-1,3,2-dioxaborin) molecules: a trans-to-cis-isomerization-induced structural transition studied with STM[END_REF]. Additionally, they reported that the application of a mild electric field induced the formation of bilayer structure of 1,3,6,8-tetrakis(1-butyl-1H-1,2,3-triazol-4-yl)pyrene molecules on top of a trimesic acid network [START_REF] Zheng | Bilayer molecular assembly at a solid/liquid interface as triggered by a mild electric field[END_REF].

Photoresponsive molecular assemblies formed at the liquid/solid interface

Design of photoresponsive molecular assemblies

Because the liquid/solid interface is an ideal platform to study 2D supramolecular chemistry, the photoresponsive behavior of molecular assemblies composed of photochromic compounds at the liquid/solid interface has recently attracted interest. Although strong quenching of photoreactions is usually observed on metal surfaces [START_REF] Thomas | Chromophore-functionalized gold nanoparticles[END_REF], some photoreactions have been reported to occur on HOPG [START_REF] Tahara | Tailoring surface-confined nanopores with photoresponsive groups[END_REF].

Upon irradiation, photochemical reactions can change the concentration of the solute in the solution and induce changes in the assembly formed at the liquid/solid interface. The ordering transformation occurs by the exchange of molecules between the interface and the solution; thus, understanding of the process of 2D self-assembly is important to control the photoinduced ordering transformation (Fig. 3). The adsorbabilities of different molecules on a substrate are different, and quantitative characterization of the adsorption process is important. A large variety of patterns have been reported: single rows, double rows, rosettes, porous networks, honeycombs, etc. The ordering formation at the interface can be regarded as 2D crystallization; thus, the pattern is determined by the molecular structure of the components. The central point in the design of an efficient photoresponsive monolayer at the liquid/solid interface lies in the choice of the photochromic units. To date, existing systems have been based on the photodecomposition of diazoanthrone [START_REF] Heinz | Photodecomposition of 10-diazo-2-hexadecylanthrone on graphite studied by scanning tunneling microscopy[END_REF] or the photoisomerization of thioindigo [START_REF] Petersen | Monolayers of tetrachloro-thioindigo and thioindigo in the STM: orientational disorder and the absence of photochromism[END_REF],

anthracene dimer [START_REF] Kikkawa | Two-dimensional structures of anthracene derivatives: photodimerization and host-guest chemistry[END_REF], azobenzene [START_REF] Vanoppen | Solvent codeposition and cis-trans isomerization of isophthalic acid derivatives studied by STM[END_REF][START_REF] Feng | Completely interfacial photoisomerization of 4-hydroxy-3′-trifluoromethyl-azobenzene studied by STM on HOPG[END_REF][START_REF] Shen | Submolecular observation of photosensitive macrocycles and their isomerization effects on host-guest network[END_REF][START_REF] Zeitouny | Photoinduced structural modifications in multicomponent architectures containing azobenzene moieties as photoswitchable cores[END_REF][START_REF] Bléger | Photoswitching vertically oriented azobenzene self-assembled monolayers at the solid-liquid interface[END_REF][START_REF] Shen | Switchable ternary nanoporous supramolecular network on photo-regulation[END_REF][START_REF] Zhang | Photo-induced polymerization and isomerization on the surface observed by scanning tunneling microscopy[END_REF][START_REF] Zhang | Two-dimensional networks of an azobenzene derivative: bi-pyridine mediation and photo regulation[END_REF][START_REF] Tahara | Tailoring surface-confined nanopores with photoresponsive groups[END_REF], stilbene [START_REF] Zhang | Two-dimensional networks of an azobenzene derivative: bi-pyridine mediation and photo regulation[END_REF][START_REF] Liao | STM investigation of the photoisomerization and photodimerization of stilbene derivatives on HOPG surface[END_REF], diarylethene [START_REF] Arai | Reversible photoinduced change in molecular ordering of diarylethene derivatives at a solution-HOPG interface[END_REF][START_REF] Sakano | Formation of two-dimensionally ordered diarylethene annulated isomer at the liquid/HOPG interface upon in situ UV irradiation[END_REF][START_REF] Bonacchi | Surface-induced selection during in situ photoswitching at the solid/liquid interface[END_REF][START_REF] Yokoyama | Phototriggered formation and disappearance of surface-confined self-assembly composed of photochromic 2-thienyl-type diarylethene: a cooperative model at the liquid/solid interface[END_REF][START_REF] Frath | Diarylethene self-assembled monolayers: cocrystallization and mixing-induced cooperativity highlighted by scanning tunneling microscopy at the liquid/solid interface[END_REF][START_REF] Yokoyama | Effects of alkyl chain length and hydrogen bonds on the cooperative self-assembly of 2-thienyl-type diarylethenes at a liquid/highly oriented pyrolytic graphite (HOPG) interface[END_REF][START_REF] Maeda | Rational design of highly photoresponsive surface-confined self-assembly of diarylethenes: reversible three-state photoswitching at the liquid/solid interface[END_REF][START_REF] Maeda | Discrimination between conglomerates and pseudoracemates using surface coverage plots in 2-D self-assemblies at the liquid/graphite interface[END_REF], or terthiophene [START_REF] Yokoyama | Photoinduced four-state three-step ordering transformation of photochromic terthiophene at a liquid/solid interface based on two principles: photochromism and polymorphism[END_REF] (Fig. 4). The majority of the systems that have been studied to date have been based on the azobenzene photochromic unit. Azobenzene compounds are well known to undergo photoisomerization between cis and trans isomers. The same behavior is observed for stilbene derivatives. However, stilbene can also undergo a [2+2] photodimerization that leads to the formation of a substituted cyclobutane [START_REF] Liao | STM investigation of the photoisomerization and photodimerization of stilbene derivatives on HOPG surface[END_REF]. The isomerization from the trans to the cis form can be induced by UV light irradiation. The opposite isomerization occurs via visible light irradiation.

Thermal treatment also induces cis to trans isomerization. The major drawback of azobenzene and stilbene is the small difference between the absorption spectra of their two isomers, which makes selective irradiation difficult. Consequently, trans-to-cis and cis-to-trans isomerization usually occur concomitantly upon irradiation.

Diarylethene and terthiophene are a different type of photochromic unit, which usually undergo an electrocyclic reaction between the open-and closed-ring isomers. Selective irradiation of each isomer is usually possible due to the greater differences in their absorption compared to trans-cis photochromophores. Another advantage is the higher thermal stability of the open-and closed-ring isomers, which can usually be isolated and studied independently. Sometimes, a side reaction leads to the formation of a by-product known as an annulated-ring isomer, which can form an ordering of its own (vide infra).

Photoresponsive molecular assemblies based on trans-cis isomerization

Upon irradiation of a solution containing the azobenzene trans isomer with UV light, a photostationary state containing both the cis and trans isomers is obtained. A solution of pure cis isomer is never obtained due to the lack of selectivity in the irradiation.

De Schryver and co-workers reported that after the deposition of a photostationary state mixture, domains of both trans and cis isomers were observed simultaneously and characterized by the differences in their lattice parameters and the orientation of their respective 2D crystal phases [START_REF] Vanoppen | Solvent codeposition and cis-trans isomerization of isophthalic acid derivatives studied by STM[END_REF]. Another study by Jiang and co-workers reported that in-situ irradiation led to a monolayer composed solely of the cis isomer [START_REF] Feng | Completely interfacial photoisomerization of 4-hydroxy-3′-trifluoromethyl-azobenzene studied by STM on HOPG[END_REF]. In that case, no thermal cis-to-trans back reaction was observed at the interface. This can be explained by the energetically favored ordering of the cis isomer compared to that of the trans isomer. Indeed, the cis isomer geometry facilitates the formation of a hydrogen bond network, and the denser packing increases van der Waals interactions.

A strategy to control the inclusion of a coronene guest into a nanoporous network was developed by Wang and co-workers [START_REF] Shen | Submolecular observation of photosensitive macrocycles and their isomerization effects on host-guest network[END_REF]. The shape and size of the pores could be tuned by appropriate light irradiation of the bi-component monolayers composed of TCBD and 4NN-Macrocycle 1 (1,2,17,18,33,34,48,49-octaaza- [START_REF] Münninghoff | Chemistry at the square nanometer: reactivity at liquid/solid interfaces revealed with an STM[END_REF](4,4ʹ)cyclophane-1,17,33,48-tetraene), which contains four azobenzene groups. Reversible control of the adsorption/exclusion of the coronenes inside/outside the pores was also achieved (Fig. 5) [START_REF] Shen | Switchable ternary nanoporous supramolecular network on photo-regulation[END_REF]. Modellization based on molecular mechanics/molecular dynamics (MM/MD) calculations was used to simulate the orderings obtained for the corresponding multi-component assemblies. The same group developed a monolayer, based on azobenzene-diacetylene derivative 2, in which two types of photocontrol are possible by changing the wavelength of the irradiation light (Fig. 6) [START_REF] Zhang | Photo-induced polymerization and isomerization on the surface observed by scanning tunneling microscopy[END_REF]. By irradiation with 254 nm light, a polymerization of the diacetylene units on the lateral chains could be initiated. Reversible switching between the trans and cis isomers was controlled by alternate irradiation with 365 nm and 435 nm light at the phenyloctane/HOPG interface. Copyright 2012 American Chemical Society.

The same group reported a bi-component system fabricated with tetraacidic azobenzene and dipyridylethene that could be reversibly regulated by irradiation with UV and visible light [START_REF] Zhang | Two-dimensional networks of an azobenzene derivative: bi-pyridine mediation and photo regulation[END_REF]. An example consisting of pure stilbene monolayers was also reported (Fig. 7) [START_REF] Zhang | Two-dimensional networks of an azobenzene derivative: bi-pyridine mediation and photo regulation[END_REF]. The groups of Tobe and De Feyter collaborated on a study of nanoporous monolayers obtained from dehydrobenzo [START_REF] Bonifazi | Supramolecular chemistry at interfaces: molecular recognition on nanopatterned porous surfaces[END_REF]annulene (DBA) 5, which bears three azobenzene units that form a central hexagonal pore (Fig. 8) [START_REF] Tahara | Tailoring surface-confined nanopores with photoresponsive groups[END_REF]. In that case, no significant transition between different molecular orderings was observed upon irradiation. However, the inclusion of a guest coronene molecule inside the central pore was controlled by light. Prior to irradiation, most pores were occupied by only one coronene guest molecule. In-situ UV irradiation induced a trans-cis isomerization that increased the size of the central pores, allowing them to host two (16.3% of occurrence), three (2.9%), and up to four (0.2%) coronene molecules. Reversible control was

Photoresponsive molecular assemblies based on electrocyclic reactions

Generally, the individual isomers of diarylethenes and terthiophenes can be isolated and studied independently due to their high stabilities. Moreover, irradiation usually leads to photostationary states containing predominantly the open-or closed-ring isomer, due to the high conversion ratio of the electrocyclic reactions. Occasionally, side photoreactions can form the annulated-ring isomer and lead to multiple ordering transformations.

The first example of the use of diarylethene in reversible switching between two stable orderings was achieved by our group, in which a diarylethene-pyrene dyad and a diarylethene-pyrene-diarylethene triad were analyzed on phenyloctane/HOPG and octanoic acid/HOPG interfaces, respectively (Fig. 9) [START_REF] Arai | Reversible photoinduced change in molecular ordering of diarylethene derivatives at a solution-HOPG interface[END_REF]. The in-situ formation of the annulated-ring isomer molecular ordering was also reported for the first time by our group for diarylethene 7 (Fig. 10) [START_REF] Sakano | Formation of two-dimensionally ordered diarylethene annulated isomer at the liquid/HOPG interface upon in situ UV irradiation[END_REF]. A two-step transition between three Lateral ester alkyl chains sufficiently stabilized molecular ordering for a similar diarylethene reported recently by Cechini, Hecht, Samorì, and co-workers [START_REF] Bonacchi | Surface-induced selection during in situ photoswitching at the solid/liquid interface[END_REF]. A two-step transition was again observed for diarylethene 8, and reversible transition between isomers 8o and 8c was even possible (Fig. 11). A theoretical model was used to determine the adsorption energy, intermolecular interaction energy, and total energy per molecule per unit cell of the diarylethene monolayers. The annulated-ring isomer 8a adsorbed most favorably on the surface due to the higher stability of its molecular ordering, which was highlighted by the simulated values (Table 1). Table 1. Estimated thermodynamic quantities for the isomers of diarylethene 8. Eads is the adsorption energy, Einter the interaction energy with the neighboring molecules, Euc/A the total energy per molecule normalized by the unit cell area, and γ the free energy excess considering both energetic and entropic contributions. the formation of polymorphs (Fig. 12) [START_REF] Yokoyama | Photoinduced four-state three-step ordering transformation of photochromic terthiophene at a liquid/solid interface based on two principles: photochromism and polymorphism[END_REF]. The closed-ring isomer 9c did not exhibit any ordering, but in-situ irradiation with visible light induced the formation of the open-ring isomer 9o, which provided two polymorphs (orderings α and β) depending on its concentration. Irradiation with UV light led to the formation of an annulated-ring isomer 9a that exhibited the characteristic honeycomb molecular ordering γ. In addition to the ability to control the transition between multiple states, sensitivity to the stimulus is another important aspect of an efficient photoresponsive system. A high rate of exchange at the liquid/solid interface and cooperativity in the adsorption process are two parameters that can contribute to the creation of highly stimuli-responsive systems.

E ads [kcal mol -1 ] E inter /2 [kcal mol -1 ] E uc /A [kcal mol -1 nm -2 ] γ [kcal mol -1 nm -2 ] 8o -
Inspired by cooperative supramolecular polymerization in solution [START_REF] Zhao | Nucleation-elongation: a mechanism for cooperative supramolecular polymerization[END_REF][START_REF] De Greef | Supramolecular polymerization[END_REF], our group has recently developed a model of the equilibrium at the liquid/solid interface and used this model to investigate the formation of 2D molecular orderings [START_REF] Yokoyama | Phototriggered formation and disappearance of surface-confined self-assembly composed of photochromic 2-thienyl-type diarylethene: a cooperative model at the liquid/solid interface[END_REF][START_REF] Yokoyama | Effects of alkyl chain length and hydrogen bonds on the cooperative self-assembly of 2-thienyl-type diarylethenes at a liquid/highly oriented pyrolytic graphite (HOPG) interface[END_REF][START_REF] Nishitani | Investigation on the surface-confined self-assembly stabilized by hydrogen bonds of urea and amide groups: quantitative analysis of concentration dependence of surface coverage[END_REF][START_REF] Nishitani | Influence of Multidirectional Interactions on Domain Size and Shape of 2-D Molecular Assemblies[END_REF]. The model considers two different equilibrium constants, the nucleation (Kn) and elongation (Ke) constants, for the first nucleation step and the subsequent elongation steps described in equation 1, respectively.  is the degree of cooperativity, which is defined as the ratio of Kn/Ke. For a cooperative process, this ratio is smaller than unity. This model takes into account the intermolecular interactions between neighboring molecules on the substrate.

A ⇌ A A A ⇌ A A A ⇌ A ⋮ A A ⇌ A 1
The parameters can be obtained by the fitting the concentration dependence of the surface coverage using equation 2,

θ 1 θ σ θ 1 θ , where α ⋅ ⋅ 2
where ct is the total concentration, Asub is the total area of the substrate, L is the volume of the supernatant solution, NA is the Avogadro constant, and S is the unit area occupied by one molecule on the substrate.

Diarylethene 10 was used to achieve reversible assembly/disassembly triggered by light at the octanoic acid/HOPG interface (Fig. 13) [START_REF] Yokoyama | Phototriggered formation and disappearance of surface-confined self-assembly composed of photochromic 2-thienyl-type diarylethene: a cooperative model at the liquid/solid interface[END_REF]. This result demonstrated that the use of a cooperative adsorption process can enable highly sensitive photocontrol over 2D ordering. The equilibrium constants for the elongation, nucleation, and degree of cooperativity for diarylethene 10 were found to be Ke = 4600 M -1 , Kn = 2.1 M -1 , and σ = 5 × 10 -4 , respectively [START_REF] Yokoyama | Effects of alkyl chain length and hydrogen bonds on the cooperative self-assembly of 2-thienyl-type diarylethenes at a liquid/highly oriented pyrolytic graphite (HOPG) interface[END_REF]. The adsorption parameters for each isomer of diarylethene 7 were determined by fitting the simulated curves from the cooperative model with the experimental STM data at the octanoic acid/HOPG interface (Fig. 14, Table 2) [START_REF] Frath | Diarylethene self-assembled monolayers: cocrystallization and mixing-induced cooperativity highlighted by scanning tunneling microscopy at the liquid/solid interface[END_REF]. The high equilibrium constant of elongation observed for the annulated-ring isomer 7a rationalized the previously reported favorability of the formation of this molecular ordering upon in-situ irradiation with UV light [START_REF] Sakano | Formation of two-dimensionally ordered diarylethene annulated isomer at the liquid/HOPG interface upon in situ UV irradiation[END_REF]. The cooperative model also

Conclusions and perspectives

In the field of photochemical control of surface-adsorbed molecular layers, considerable advances have been recently achieved using STM. In particular, remarkable advances have been made in photoresponsive self-assemblies at the liquid/solid interface using a supramolecular chemistry approach. High-level control of the transition between several stable molecular orderings has become possible by controlling the adsorption process of each photochromic isomer. Moreover, elaborate supramolecular structures can be controlled using molecular recognition. Additionally, a better understanding of their physisorption properties was made possible by the use of various theoretical models.

The packing structures of an assembly at the interface can be reproduced using MM/MD simulations, but it is still difficult to predict the whole packing from only the molecular structure.

From our experience, alkyl chains with amide groups contribute to the formation of stable assemblies at the interface. The nucleation and elongation equilibrium constants have been revealed to be related to the molecular structure, but they are also difficult to predict from only the molecular structure. For example, the reason for the very strong adsorption of the annulated-ring isomer 7a cannot be understood from its molecular structure. However, photochemical modulation of the molecular structure does affect its packing structure and the equilibrium constants, making photocontrol of the assembly possible.

In the case of diarylethene 10, the open-ring isomer aligns at the interface in a parallel conformation that is not photoreactive, making photoreaction at the interface impossible. The photoisomerization is believed to occur in the supernatant solution phase. However, the photoisomerization of azobenzene 5 is believed to occur at the interface. The excited state of the adsorbate is reported to be effectively quenched by the surface. The detailed dynamics of the photoexcited molecule at the surface or interface are still not completely understood, and have been attracting interest.

There is still room for improvement and innovation towards sophisticated photoresponsive systems. Adsorption at the liquid/solid interface is a supramolecular process, and thus many strategies that are used in supramolecular chemistry in solution can be applied. The structureproperty relationships of the adsorption process are not clear enough. The effect of the solvent and the substrate should also be investigated more systematically to facilitate development toward practical applications. With this knowledge, photoresponsive surfaces with appropriate sensitivity and fast response time could be developed for practical applications in several fields, such as optoelectronic devices, molecular nanomaterials, and even heterogeneous catalytic systems.

Fig. 1 .

 1 Fig. 1. Structure of an azobenzene derivative, and STM images after switching many molecules to the cis state by scanning at a sufficiently elevated bias voltage. The cis isomers are arranged in a periodic pattern, forming a lattice. (a) STM image and (b) unit cell of the cis isomers. Reprinted with permission from reference 47. Copyright 2008 Macmillan Publishers Ltd.

Fig. 2 .

 2 Fig. 2. Schematic drawing of the cooperative switching of a small domain of 4ʹ-(biphenyl-4-ylazo)-biphenyl-4-thiol immobilized on a Au surface. Intermolecular interactions between adjacent molecules stabilize the packing of domains consisting exclusively of trans isomers, as well as the packing of domains consisting exclusively of cis isomers. Reprinted with permission from reference 56. Copyright 2007 National Academy of Sciences of the USA.

Fig. 3 .

 3 Fig. 3. Schematic drawing of a phototriggered ordering transformation at the liquid/solid interface.

Fig. 4 .

 4 Fig. 4. General chemical structures of photochromic units used in the design of photoresponsive monolayers.

Fig. 5 .

 5 Fig. 5. (a) High-resolution STM image of the TCDB1/1(t,t,t,t) network structure. (b) The molecular model of the TCDB1/1(t,t,t,t) structure. (c) STM image of the ternary adlayer of TCDB1/1(t,t,t,t)/coronene before UV irradiation. (d) The molecular model of the TCDB1/1(t,t,t,t)/coronene adlayer. (e) STM image of the TCDB2/1(t,c,t,c)/coronene architecture after UV irradiation. (f) The molecular model of the ternary TCDB2/1(t,c,t,c)/coronene network. In all the molecular models, the red balls represent oxygen atoms; blue, carbon; and purple, nitrogen. The hydrogen atoms are omitted for clarity. Reprinted with permission from reference 92. Copyright 2011 American Chemical Society.

Fig. 6 .

 6 Fig. 6. STM images (scale bar = 5 nm) of (a) 2 (before irradiation), (b) 2 upon UV irradiation at 254 nm, and (c) 2 upon UV irradiation at 365 nm for 30 min. Adapted with permission from reference 93.

  The ordering transformation induced by the trans-cis isomerization of stilbenes 3 and 4 upon in-situ irradiation at the phenyloctane/HOPG interface was analyzed by STM. Brief irradiation of the compound 4 monolayer also led to the formation of the cis isomer molecular ordering. A longer irradiation time induced a [2+2] photodimerization reaction that formed cyclobutane, and led to additional changes in the molecular ordering.

Fig. 7 .

 7 Fig. 7. Photoresponsive monolayers based on stilbenes 3 and 4. Adapted with permission from reference 96. Copyright 2014 American Chemical Society.

Fig. 8 .

 8 Fig. 8. a) Structural formula of the DBA trans-5, coronene (COR), and hexakis(phenylethynyl)benzene. b) Molecular models of the honeycomb structure formed by the self-assembly of trans-5 with all-trans-azobenzene units in which a hydrogen-bonded hexamer of dicarboxyazobenzene units creates a size-and shape-confined space. c) The same pore as (b) with one of the dicarboxyazobenzene units adopting a cis configuration. Adapted with permission from reference 95. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

  Preferential adsorption of the closed-closed isomer of the triad 6c-c over the open-open isomer 6o-o or the open-closed isomer 6o-c was observed.

Fig. 9 .

 9 Fig. 9. Reversible ordering transformation between the orderings of the diarylethene derivatives 6o-o and 6c-c. Adapted with permission from reference 97. Copyright 2008 American Chemical Society.

  molecular orderings was possible due to the formation of this third isomer. The amide groups were reported to stabilize the molecular orderings through the creation of a hydrogen bond network. No molecular orderings of the open-ring isomer were observed to form for diarylethene substituted with ester groups.

Fig. 10 .

 10 Fig. 10. Chemical structures and STM images of (a) the open-ring isomer 7o (ordering α), (b) the closed-ring isomer 7c (ordering β), and (c) the annulated-ring isomer 7a (ordering γ). See references 45 and 47 for details of the orderings. Adapted with permission from reference 101. Copyright 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

Fig. 11 .

 11 Fig. 11. a) Chemical structures and UV/Vis spectra of the investigated diarylethene in its open (8o), closed (8c), and the closed form containing 60 % of (irreversible) by-product (8a). STM height images of monolayers of b) 8o, d) 8c, and f) 8a. Minimized molecular packing motifs of c) 8o, e) 8c, and g) 8a. Adapted with permission from reference 99. Copyright 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

Fig. 12 .

 12 Fig. 12. Four-state, three step ordering transformation observed for terthiophene 9. Adapted with permission from reference 105. Copyright 2008 American Chemical Society.

Fig. 13 .

 13 Fig. 13. (a) Formation and disappearance of the reversible ordering of 10 upon in-situ photoirradiation at the octanoic acid/HOPG interface. (b) The plot of surface coverage against the conversion ratio of the sample solution. Adapted with permission from reference 100. Copyright 2014 The Royal Society of Chemistry.

  revealed co-crystallization and mixing-induced cooperativity in the formation of orderings from mixtures of the isomers 7o and 7c[START_REF] Frath | Diarylethene self-assembled monolayers: cocrystallization and mixing-induced cooperativity highlighted by scanning tunneling microscopy at the liquid/solid interface[END_REF]. The two isomers 7o and 7c influence each other during the formation of molecular orderings, and form mixed crystals. Moreover, mixing-induced cooperativity in the ordering formation process was observed in the STM measurements; the closed-ring isomer 7c can induce cooperativity in the formation of orderings that are mainly composed of the open-ring isomer 7o. It was revealed that mixing of the components influences the formation of 2D orderings at the liquid/solid interface.

Fig. 14 .

 14 Fig. 14. (a) Concentration dependence of the surface coverage of 7o, 7c, and 7a at the octanoic acid/HOPG interface. Concentration dependence of the surface coverage of (b) ordering  for 7c and mixtures of 7o/7c (37:63 and 51:49) and of (c) ordering  for 7o and a mixture of 7o/7c (78:22). Adapted with permission from reference 101. Copyright 2015 Wiley-VCH Verlag GmbH & Co.KGaA.

Table 2 .

 2 Best-fit adsorption parameters for 7o, 7c, and 7a at the octanoic acid/HOPG interface

		K e [M -1 ]	K n [M -1 ]	σ
	7o	6.8 × 10 4	6.4 × 10 4	0.95
	7c	6.6 × 10 4	≤ 6.6 × 10 -2	≤ 1 0 -6
	7a	1.5 × 10 6	≤ 1.5	≤10 -6

Acknowlegements

This review included our original works supported by Grant-in-Aid for Scientific Research on Innovative Areas "Photosynergetics" (JSPS KAKENHI Grant Number JP26107008) from MEXT, Japan.