Joseph Le Roux
email: joseph.leroux@lipn.fr

Antoine Rozenknop
email: antoine.rozenknop@lipn.frjfoster@computing.dcu.ie

Jennifer Foster

Combining PCFG-LA Models with Dual Decomposition: A Case Study with Function Labels and Binarization

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Introduction

Because of the large amount of possibly contradictory information contained in a treebank, learning a phrase-structure-based parser implies making several choices regarding the prevalent annotations which have to be kept -or discarded -in order to guide the learning algorithm. These choices, which include whether to keep function labels and empty nodes, how to binarize the trees and whether to alter the granularity of the tagset, are often motivated empirically by parsing performance rather than by the different aspects of the language they may be able to capture.

Recently Rush et al. (2010), [START_REF] André | Dual decomposition with many overlapping components[END_REF] and [START_REF] Koo | Dual decomposition for parsing with non-projective head automata[END_REF] framework for combining different types of NLP tasks or for building parsers from simple slave processes that only check partial well-formedness. Here we propose to follow this idea, but with a different objective. We want to mix different parsers trained on different versions of a treebank each of which makes some annotation choices in order to learn more specific or richer information. We will use state-of-the-art unlexicalized probabilistic contextfree grammars with latent annotations (PCFG-LA) in order to compare our approach with a strong baseline of high-quality parses. Dual Decomposition is used to mix several systems (between two and four) that may in turn be combinations of grammars, here products of PCFG-LAs [START_REF] Petrov | Products of random latent variable grammars[END_REF]. The systems being combined make different choices with regard to i) function labels and ii) grammar binarization.

Common sense would suggest that information in the form of function labels -syntactic labels such as SBJ and PRD and semantic labels such as TMP and LOC -might help in obtaining a fine-grained analysis. On the other hand, the independence hypothe-sis on which CFGs rely and on which most popular parsers are based may be too strong to learn the dependencies between functions across the parse trees. Also, the number of parameters increases with the use of function labels and this can affect the learning process.

At first glance, binarization need not be an issue, as CFGs admit a binarized form recognizing exactly the same language. But binarization can be associated with horizontal markovization and in this case the recognized language will differ. Furthermore this can impose an unwanted emphasis on what frontier information is more relevant to learning (beginning or end of constituents). In the toy example of Figure 1, the original grammar consisting of a unique rule extracted from one tree only recognizes the string bcdef, while the grammar learned from the left binarized and markovized tree recognizes (among others) bcdef and bdcef and the grammar learned from the right binarized and markovized tree recognizes (among others) bcdef and bcedf.

We find that i) retaining the function labels in nonterminal categories loses its negative impact on parsing as the number of grammars increases in PCFG-LA product models, ii) the function labels themselves can be recovered with near state-of-the-artaccuracy, iii) combining grammars with and without function labels using dual decomposition is beneficial, iv) combining left and right-binarized grammars using dual decomposition also leads to better trees and, v) our best results (a Parseval labeled F-score of 92.4, a Stanford labeled attachment score (LAS) of 93.0 and a penn2malt unlabeled attachment score (UAS) of 94.3 on Section 23 of the Wall Street Journal) are obtained by combining three grammars which encode different function label/binarization decisions.

The paper is organized as follows. § 2 reviews related work. § 3 presents approximate PCFG-LA parsers as linear models, while § 4 shows how we can use dual decomposition to derive an algorithm for combining these models. Experimental results are presented and discussed in § 5.

Related Work

Parser Model Combination It is well known that improved parsing performance can be achieved by leveraging the alternative perspectives provided by several parsing models rather than relying on just one. Examples are parser co-training [START_REF] Steedman | Bootstrapping statistical parsers from small datasets[END_REF][START_REF] Sagae | Dependency parsing and domain adaptation with LR models and parser ensembles[END_REF], voting over phrase structure constituents or dependency arcs [START_REF] Henderson | Exploiting diversity in natural language processing: Combining parsers[END_REF][START_REF] Sagae | Dependency parsing and domain adaptation with LR models and parser ensembles[END_REF][START_REF] Surdeanu | Ensemble models for dependency parsing: Cheap and good?[END_REF], dependency parsing stacking [START_REF] Nivre | Integrating graph-based and transition-based dependency parsers[END_REF], product model PCFG-LA parsing [START_REF] Petrov | Products of random latent variable grammars[END_REF], using dual decomposition to combine dependency and phrase structure models (Rush et al., 2010) or several nonprojective dependency parsing models [START_REF] Koo | Dual decomposition for parsing with non-projective head automata[END_REF][START_REF] André | Dual decomposition with many overlapping components[END_REF], and using expectation propagation, a related approach to dual decomposition, to combine lexicalized, unlexicalized and PCFG-LA models [START_REF] Hall | Training factored PCFGs with expectation propagation[END_REF]. In this last example, the models must factor in the same way: in other words, the grammars must use the same binarization scheme. In our study, we employ PCFG-LA product models with dual decomposition, and we relax the constraints on factorization, as we require only a loose coupling of the models.

Function Label Parsing Although function labels have been available in the Penn Treebank (PTB) for almost twenty years [START_REF] Marcus | The penn treebank: Annotating predicate argument structure[END_REF], they have been to a large extent overlooked in English parsing research -most studies that report parsing results on Section 23 of the Wall Street Journal (WSJ) use parsing models that are trained on a version of the WSJ trees where the function labels have been removed. Notable exceptions are [START_REF] Merlo | Accurate function parsing[END_REF] and [START_REF] Gabbard | Fully parsing the penn treebank[END_REF] who each trained a parsing model on a version of the PTB with function labels intact. [START_REF] Gabbard | Fully parsing the penn treebank[END_REF] found that parsing accuracy was not affected by keeping the function labels. There have also been attempts to use machine learning to recover the function labels post-parsing [START_REF] Blaheta | Assigning function tags to parsed text[END_REF][START_REF] Chrupala | Better training function labeling[END_REF]. We recover function labels as part of the parsing process, and use dual decomposition to combine parsing models with and without function labels. We are not aware of any other work that leverages the benefits of both types of models.

Grammar Binarization [START_REF] Matsuzaki | Probabilistic CFG with latent annotations[END_REF] compare binarization strategies for PCFG-LA parsing, and conclude that the differences between them have a minor effect on parsing accuracy as the num-ber of latent annotations increases beyond two. [START_REF] Hall | Training factored PCFGs with expectation propagation[END_REF] are forced to use head binarization when combining their lexicalized and unlexicalized parsers. Dual decomposition allows us to combine models with different binarization schemes.

Approximation of PCFG-LAs as Linear Models

In this section, we explain how we can use PCFG-LAs to devise linear models suitable for the dual decomposition framework.

PCFG-LA

Let us recall that PCFG-LAs are defined as tuples G = (N , T , H, R H , S, p) where:

• N is a set of observed non-terminals, among which S is the distinguished initial symbol,

• T is a set of terminals (words),

• H is a set of latent annotations or hidden states,

• R H is a set of annotated rules, of the form • p : R H → R ≥0 defines the probabilities associated with rules conditioned on their left-hand side. Like [START_REF] Petrov | Improved inference for unlexicalized parsing[END_REF], we impose that the initial symbol S has only one latent annotation. In other words, among rules with S on the left-hand side, only those of the form

a[h 1 ] → b[h 2 ] c[h 3 ] for internal
S[0] → γ are in R H .
With such a grammar G we can define probabilities over trees in the following way. We will consider two types of trees, annotated trees and skeletal trees. An annotated tree is a sequence of rules from R H , while a skeletal tree is a sequence of skeletal rules from R. An annotated tree T H is obtained by left-most derivation from S[0]. Its probability is:

p(T H ) = r∈T H p(r) (1)
We define a projection ρ from annotated trees to skeletal trees. ρ(T H ) is a tree T isomorphic to T H with the same terminal and non-terminal symbols labeling nodes, without hidden states. The probability of a skeletal tree T is a sum of the probabilities of all annotated trees that admit T as their projection.

p(T ) = T H ∈ρ -1 (T ) r∈T H p(r) (2)
PCFG-LA parsing amounts to, given a sequence of words, finding the most probable skeletal tree with this sequence as its yield according to a grammar G:

T * = arg max T T H ∈ρ -1 (T ) r∈T H p(r) (3)
Because of this alternation of sum and products, the parsing problem is intractable. Moreover, the PCFG-LAs do not belong to the family of linear models that are assumed in the Lagrangian framework of [START_REF] Rush | A tutorial on dual decomposition and lagrangian relaxation for inference in natural language processing[END_REF]. We now turn to approximations for the parsing problem in order to address both issues.

Variational Inference and MaxRule

Variational inference is a common technique to approximate a probability distribution p with a cruder one q, as close as possible to the original one, by minimizing the Kullback-Liebler divergence between the two -see for instance [START_REF] Smith | Linguistic Structure Prediction[END_REF], chapter 5 for an introduction. [START_REF] Matsuzaki | Probabilistic CFG with latent annotations[END_REF] showed that one can easily find such a cruder distribution for PCFG-LAs and demonstrated experimentally that this approximation gives good results. More precisely, they find a PCFG that only recognizes the input sentence where the probabilities q(r s ) of the rules are set according to their marginal probabilities in the original PCFG-LA parse forest. The parameters r s are skeletal rules with span information. Distribution q is defined in Figure 2.

Other approximations are possible. In particular, [START_REF] Petrov | Improved inference for unlexicalized parsing[END_REF] found that normalizing by the forest probability (in other words the inside probability of the root node) give better exper-

score(a → b c, i, j, k) = x,y,z∈H P i,k out a[x] • p a[x] → b[y] c[z] • P i,j in b[y] • P j,k in c[z] norm(a → b c, i, j, k) = x∈H P i,k in a[x] • P i,k out a[x] score(a → w, i) = x∈H P i,i out a[x] • p a[x] → w norm(a → w, i) = x∈H P i,i in a[x] • P i,i out a[x] q(rs) = score(rs) norm(rs) (Variational Inference) or score(rs) P 0,n in (S[0]) (MaxRule-Product)
Figure 2: Variational Inference for PCFG-LA. P in and P out denote inside and outside probabilities.

imental results although its interpretation as variational inference is still unclear. This approximation is called MaxRule-Product and amounts to replacing the norm function (see Figure 2). In both cases, the probability of a skeletal tree now becomes a simple product of parameters associated with anchored skeletal rules. For our purpose, the consequence is twofold:

1. The parsing problem becomes tractable by applying standard PCFG algorithms relying on dynamic programming (CKY for example).

2. Equivalent to probability, a score σ can be defined as the logarithm of the probability. The parsing problem becomes2 :

T * = arg max T rs∈T q(r s ) = arg max T rs∈T log q(r s ) = arg max T rs∈F w rs • 1{r s ∈ T } = arg max T σ(T )
Thus, from a PCFG-LA we are able to define a linear model whose parameters are the logprobabilities of the rules in distribution q.

Products of PCFG-LAs

Although PCFG-LA training is beyond the scope of this paper, it is worthwhile mentioning that the most common way to learn their parameters relies on Expectation-Maximization which is not guaranteed to find the optimal estimation. Fortunately, this can be partly overcome by combining grammars that only differ on the initial parameterization of the EM algorithm. The probability of a skeletal tree is the product of the probabilities assigned by each single grammar G i .

T * = arg max T n i=1 q G i (T ) (4)
Since grammars only differ by their numerical parameters (i.e. skeletal rules are the same), inference can be efficiently implemented using dynamic programming [START_REF] Petrov | Products of random latent variable grammars[END_REF].

Scoring with n such grammars now becomes:

T * = arg max T n i=1 r∈T log q G i (r) (5) = arg max T r∈T n i=1 log q G i (r) (6)
The distributions q G i still have to be computed independently -and possibly in parallel -but the final decoding can be performed jointly. This is still a linear model for PCFG-LA parsing, but restricted to grammars that share the same skeletal rules.

In this section, we show how we derive an algorithm to work out the best parse according to a set of n grammars that do not share the exact same skeletal rules. As such, the grammars' product cannot be easily conducted inside the parser to produce and score a same and unique best tree, and we now consider a c(ompound)-parse as a tuple (T 1 . . . T n ) of n compatible trees. Each grammar G i is responsible for scoring tree T i , and we seek to obtain the c-parse that maximizes the sum of the scores of its different trees. For a c-parse to be consistent, we have to precisely define the parts on which the trees must agree to be compatible with each other, so that we can model these as agreement constraints.

Compound Parse Consistency

Let us suppose we have a set of phrase-structure parsers trained on different versions of the same treebank. Hence, some elements in the charts will either be the same or can be mapped to each other provided an equivalence relation and we define consensus between parsers on these elements.

When the grammar is not functionally annotated, phrase-structure trees can be decomposed into a set of anchored (syntactical) categories X s , asserting that a category X is in the tree at position3 s. Thus, such a tree T can be described by means of a boolean vector z(T ) indexed by anchored labels X s , where z(T ) Xs = 1 if X s is in T and 0 otherwise.

We will differentiate the set of natural nonterminals that occur in the treebanks from the set of artificial non-terminals that do not occur in the treebank and are the results of a binarization with markovization. As these artificial non-terminals disappear after reversing binarization in solution trees, they do not play any role in the consensus between parsers, and we only consider natural non-terminals in the set of anchored labels.

When the grammar is functionally annotated, each label X in a tree is a pair (X, F ), where X is a syntactical category and F is a function label. In this case, in order to manage the consensus with non-functional grammars, we decompose such a tree into two sets: a set of anchored categories X s and a set of anchored function labels F s . Thus, a tree T can be described by means of two boolean vectors:

• z(T ) indexed by anchored categories X s , z(T ) Xs = 1 if there exists a function label F so that (X, F ) s is in T , and 0 otherwise;

• ζ(T ) indexed by anchored function labels F s , ζ(T ) Fs = 1 if there exists a category X so that (X, F ) s is in T , and 0 otherwise.

In the present work, a compound parse (T 1 . . . T n ) is said to be consistent iff every tree shares the same set of anchored categories, i.e. iff:

∀(i, j) ∈ 1, n 2 , z(T i ) = z(T j )

Combining Parsers through Dual Decomposition

Like previous applications, we base our reasoning on the assumption that computing the optimal score with each grammar G i can be efficiently calculated, which is the case for approximate PCFG-LA parsing. We follow the presentation of the decomposition from [START_REF] André | Dual decomposition with many overlapping components[END_REF] to explain how we can combine several PCFG-LA parsers together. For a sentence s, we want to obtain the best consistent compound parse from a set of n parsers:

(P ) : find arg max (T 1 ...Tn)∈C n p=1 σ p (T p ) (7) s.t. ∀(i, j) ∈ 1, n 2 , z(T i ) = z(T j ) (8)
where

C = F 1 (s) × ... × F n (s)
is the product of parse forests F i (s), and F i (s) is the set of trees in grammar G i whose yields are the input sentence s.

Solving this problem with an exact algorithm is intractable. While artificial nodes could be inferred using a traditional parsing algorithm based on dynamic programming (i.e. CKY), the natural nodes require a coupling of the parsers' items to enforce the fact that natural daughter nodes must be identical (or equivalent) with the same spans for all parsers. Since the debinarization of markovized rules enables the creation of arbitrarily long n-ary rules, in the worst case the number of natural daughters to check is exponential in the size of the span to infer. Even if we bound the length of debinarized rules, the problem is hardly tractable.

As this problem is intractable, even for approximate PCFG-LA parsing, we apply the iterate method presented in [START_REF] Komodakis | MRF optimization via dual decomposition: Message-passing revisited[END_REF] for MRFs, also applied for joint tasks in NLP such as combined parsing and POS tagging in (Rush et al., 2010).

First, we introduce a witness vector u in order to simplify constraints in (8). Problem (P ) can then be written in an equivalent form :

(P ) : find o P = max (T 1 ...Tn)∈C n i=1 σ i (T i ) (9) s.t. ∀i ∈ 1, n , z(T i ) = u (10)
Next, we proceed to a Lagrangian decomposition. This decomposition is a two-step process:

Step 1 (Relaxation): the coupling constraints (10) are removed by introducing a vector of Lagrange multipliers Λ i = (λ i,Xs ) Xs for each parser i, indexed by anchored categories X s , and writing the equivalent problem:

(RP ) : o RP = max u, T 1...n min Λ f (u, T 1...n , Λ)
where:

f (u, T 1...n , Λ) = i σ i (T i ) + i (z(T i ) -u) • Λ i
Intuitively, we can see the equivalence of (RP ) and (P ) with the following reasoning:

• whenever all constraints (10) are met, the second sum in f is nullified and f (u, T 1...n , Λ) = i σ i (T i ), which is a finite value and precisely the objective function maximized in (P );

• if there is at least one (i, X, s) such that z(T i ) Xs = u Xs , then the value of i (z(T i )u) • Λ i can be made arbitrarily small by an appropriate choice of λ i,Xs ; in this case, min Λ f (u, T 1...n , Λ) = -∞. Thus, (RP ) can not reach its maximum at a point where constraints (10) are not satisfied.

Step 2 (dualization): the dual problem (LP ) is obtained by permuting max and min in (RP ):

(LP 1) : o LP = min Λ max u, T 1...n f (u, T 1...n , Λ)
Finally, u can be removed from (LP 1) by adding the constraint:

i Λ i = 0. As a matter of fact, one can see that if this constraint is not matched, max u,T 1...n f (u, T 1...n , Λ) = +∞ and (LP 1) can not reach its minimum on such a point. We can now find the maximum of f by maxing each T i independently of each other. The dual problem becomes:

(LP ) : o LP = min Λ n i=1 max T i ∈F i (σ i (T i ) + z(T i ) • Λ i ) s.t. i Λ i = 0
Minimization in (LP ) can be solved iteratively using the projected subgradient method. Finding a subgradient amounts to computing the optimal solution [START_REF] Rush | A tutorial on dual decomposition and lagrangian relaxation for inference in natural language processing[END_REF] for each of the n subproblems (the slave problems in the terminology of [START_REF] André | Dual decomposition with many overlapping components[END_REF] and [START_REF] Komodakis | MRF optimization via dual decomposition: Message-passing revisited[END_REF]) which can be done efficiently, by incorporating the calculation of the penalties in the parsing algorithm, and in parallel. Until the agreement constraints are met (or a maximal number of iterations τ ), the Lagrangian multipliers are updated according to the deviations from the average solutions (i.e. updates are zeros for a natural span if the parsers agree on it). This leads to Algorithm 1.

It should be noted that the DP charts are built and pruned during the first iteration only (t = 0); further iterations do not require recreating the DP chart, which is memory intensive and time consuming, nor recomputing the approximate distribution for variational inference. As DP on the pruned charts is a fast process, the bottleneck of the algorithm still is in the first calculation of slave solutions.

The stepsize sequence (α t ) 0≤t must be diminishing and non-summable, that is to say: ∀t, α t ≥ 0, lim t→∞ α t = 0 and ∞ t=0 α t = ∞. In practice, we set α t = 1 1+c(t) where c(t) is the number of times the objective function o P has increased since iterations began. Solving (P): it is easy to see that o LP is an upper bound of o P , but we do not necessarily have Algorithm 1 Find best compound parse with constraints on natural spans Require: n parsers {pi} 1≤i≤n for all i, syntactical category X, anchor s do λ (0)

i,Xs = 0 end for for t = 0 → τ do for all parsers pi do T

(t) i ← arg max T ∈F i σi(T ) + z(T ) • Λ (t) i
end for for all parsers pi do

∆ (t) i ← αt z T (t) i - 1≤j≤n z T (t) j n Λ (t+1) i ← Λ (t) i + ∆ (t) i end for if ∆ (t) i = 0 for all i then Exit loop end if end for return (T (τ ) 1 , • • • , T (τ ) n )
strong duality (i.e. o LP = o P ) due to the facts that parse forests are discrete sets. Furthermore, they get pruned independently of each other. Thus, the algorithm is not guaranteed to find a t such that z(T

(t) i )
is the same for every parser i. However -see [START_REF] Koo | Dual decomposition for parsing with non-projective head automata[END_REF] -if it does reach such a state, then we have the guarantee of having found an exact solution of the primal problem (P ). We show in the experiments that this occurs very frequently.

Experiments

Experimental Setup

We perform our experiments on the WSJ sections of the PTB with the usual split: sections 2 to 21 for training, section 23 for testing, and we run benchmarks on section 22. evalb is used for evaluation.

We use the LORG parser modified with Algorithm 1. 4 All grammars are trained using 6 split/merge EM cycles. For the handling of unknown words, we removed all words occurring once in the training set and replaced them by their morphological signature [START_REF] Attia | Handling unknown words in statistical latent-variable parsing models for Arabic, English and French[END_REF]. Grammars for products are obtained by training with 16 random seeds for each setting. We use the approximate al-gorithm MaxRule-Product [START_REF] Petrov | Improved inference for unlexicalized parsing[END_REF].

The basic settings are a combination of the two following parameters: left or right binarization: we conjecture that this affects the quality of the parsers by impacting the recognition of left and right constituent frontiers. We set vertical markovization to 1 (no parent annotation) and horizontal markovization to 0 (we drop all left/right annotations).

with or without functional annotations: in particular when non-terminals are annotated with multiple functions, all are kept.

Products of Grammars

We first evaluate each setting on its own before combining them. We test the 4 different settings on the development set, using a single grammar or a product of n grammars. Results are reported on Figure 3. We can see that right binarization performs better than left binarization. Contrary to the results of [START_REF] Gabbard | Fully parsing the penn treebank[END_REF], function labels are detrimental for parsing performance for one grammar only. However, they do not penalize performance when using the product model with 8 grammars or more. EM is not guaranteed to find the optimal model and the problem is made harder by the increased number of parameters. Product models effectively alleviate this curse of dimensionality by letting some models compensate for the errors made by others.

On the other hand, as differences between left and right binarization settings remain over all product sizes, right binarization seems more useful on its own. The first part of Table 1 gives F-score and Exact Match results of the product models with 16 grammars on the development set.

Combinations with Dual Decomposition

We now turn to a series of experiments combining product models of 16 grammars. In all these experiments, we set the maximum number of iterations in Algorithm 1 to 1000. The system then returns the first element of the c-parse. We first try to combine two settings in four different combinations:

DD Right Bin the two right-binarized systemswith and without functions -the system returns the function-labeled parse; DD Left Bin the two left-binarized systems -with and without functions -the system returns the function-labeled parse; DD Func the two systems with functions -left and right binarization -the system returns the rightbinarized parse; DD No Func the two systems without functionsleft and right binarization -the system returns the right-binarized parse;

Results are in the second part of Table 1. Unsurprisingly, the best configuration is the one combining the two best product systems (with right binarization) but all combined systems perform better than their single components. We also combine 3 and 4 parsers to see if combining the above DD Right Bin setting with information that could improve the recognition of beginning of constituents can be helpful. We have 2 settings: DD3 The 2 right-binarized parsers combined with the left binarized parser without functions,

DD4

The 4 parsers together.

In both cases the system returns the rightbinarized function annotated parse. The results are shown in the last part of Table 1. These 2 new configurations give similar F-scores, better than all 2parser configurations.

We conclude from these results that leftbinarization and right-binarization capture different linguistic aspects, even in the case of heavy horizontal markovization, and that the method we propose enables a practical integration of these models.

Table 2 shows for each setting how often the systems agree before 1000 iterations of Algorithm 1. As one might expect, the more diverse the systems are, the lower the rate of agreement.

Evaluation of Function Labeling

We also evaluate the quality of the function labels. We compare the results obtained directly from the parser output with results obtained with Funtag, a state-of-the-art functional tagger that is applied on parser output, using a gold model trained on sections 02 to 21 of the WSJ [START_REF] Chrupala | Better training function labeling[END_REF]. The results are shown in Table 3. First, we can see that the parser output is always outperformed by Funtag. This is expected from a context-free parser that has a limited domain of locality with strong independence constraints, compared to a voted-SVM classifier that can rely on arbitrarily rich features. Second, the quality of the Funtag prediction seems to be influenced by the fact that parser already handle functions and by the accuracy of the parser (Parseval F-score). This is because we use a model trained on the gold reference and so the closer the parser output is from the reference, the better the prediction. On the other hand, this is not the case with parser predicted functions, where the best system is the right-binarized product model with functions, with very similar performance obtained by the combinations consisting of 2 function parsers, settings DD Func and DD4. This tends to indicate that the constraints we have set to define consistencies in c-parses, focusing on syntactical categories, do not help in retrieving better function labels. This suggests some possible further improvements where parsers with functional annotations should be forced to agree on these too. Dependency-based evaluation of phrase structure parser output has been used in recent years to provide a more rounded view on parser performance and to compare with direct dependency parsers [START_REF] Cer | Parsing to Stanford Dependencies: Trade-offs between speed and accuracy[END_REF][START_REF] Petrov | Uptraining for accurate deterministic question parsing[END_REF][START_REF] Nivre | Evaluation of dependency parsers on unbounded dependencies[END_REF][START_REF] Foster | From news to comment: Resources and benchmarks for parsing the language of web 2.0[END_REF][START_REF] Petrov | Overview of the 2012 shared task on parsing the web[END_REF]. We evaluate our various parsing models on their ability to recover three types of dependencies: basic Stanford dependencies (de Marneffe and Manning, 2008) 5 , LTH dependencies (Johansson and Nugues, 5 We used the latest version at the time of writing, i.e. 3.20. 2007) 6 and penn2malt dependencies. 7 The latter are a simpler version of the LTH dependencies but are still used when reporting unlabeled attachment scores for dependency parsing.

Evaluation of Dependencies

The results, shown in Table 4, mirror the constituency evaluation results in that the dual decomposition results tend to outperform the basic product model results, and combining three or four grammars using dual decomposition yields the highest scores. The differences between the Func and No Func results highlight an important difference between the Stanford and LTH dependency schemes. The tool used to produce Stanford dependencies has been designed to work with phrase structure trees that do not contain function labels. In contrast, the LTH tool makes use of function label information in phrase structure trees. Thus, their availability results in only a moderate improvement in LAS for the Stanford dependencies and a very striking improvement for the LTH dependencies. By retaining function labels during parsing, we have shown that LTH dependencies can be recovered with a high level of accuracy without having to resort to a post-parsing function labeling step.

Test Set Results

We now evaluate our various systems on the test set (the first half of Table 5) and compare these results with state-of-the-art systems (the second half of Table 5). We present parser accuracy results, measured using Parseval F-score and penn2malt UAS, and, for our systems, function label accuracy for labels produced during parsing and after parsing using Funtag. We also carried out statistical significance testing 8 on the F-score differences between our various systems on the development and test sets. The results 6 nlp.cs.lth.se/software/treebank_converter. It is recommended that LTH is used with the version of the Penn Treebank which contains the more detailed NP bracketing provided by [START_REF] Vadas | Adding noun phrase structure to the penn treebank[END_REF]. However, to facilitate comparison with other parsers and dependency schemes, we did not use it in our experiments. We ran the converter with the right-Branching=false option to indicate that we are using the version without extra noun phrase bracketing. The English head-finding rules of [START_REF] Yamada | Statistical dependency analysis with support vector machines[END_REF], supplied on the website, are employed. 8 We used Dan Bikel's compare.pl script which uses stratified shuffling to compute significance. We consider a p value < 0.05 to indicate a statistically significant difference. [START_REF] Shindo | Bayesian symbol-refined tree substitution grammars for syntactic parsing[END_REF] 92.4 [START_REF] Zhang | K-best combination of syntactic parsers[END_REF] 92.3 [START_REF] Petrov | Products of random latent variable grammars[END_REF] 91.8 [START_REF] Huang | Forest reranking: Discriminative parsing with non-local features[END_REF] 91.7 [START_REF] Bohnet | A transitionbased system for joint part-of-speech tagging and labeled non-projective dependency parsing[END_REF] 93.7 We measured the performance of DD4 on the test set. It is approximately 3 times slower than the slowest product model (left binarization with function labels) and 7 slower than the fastest one (right binarization without function labels). This system performs on average 85.5 iterations of the DD algorithm. If we exclude the non-converging cases (5.1% of the cases), this drops to 39.4.

Setting

Finally we compare our results with systems trained and evaluated on the PTB, see the lower half of Table 5. Our product models are not different from those presented in [START_REF] Petrov | Products of random latent variable grammars[END_REF] and it is not surprising to see that the F-scores are similar. More interestingly our DD4 setting improves on these results and compares favorably with systems relying on richer syntactic information, such as the discriminative parser of [START_REF] Huang | Forest reranking: Discriminative parsing with non-local features[END_REF] that makes use of non-local features to score trees and the TSG parser of [START_REF] Shindo | Bayesian symbol-refined tree substitution grammars for syntactic parsing[END_REF] that can take into account larger tree fragments: this would indicate that by combining our parsers we extend the domain of locality, horizontally with binarization schemes and vertically with function labels. Our system also performs better than the combination system presented in [START_REF] Zhang | K-best combination of syntactic parsers[END_REF] that only relies on material from the PTB9 but a more detailed comparison is difficult: this system does not use products of latent models and more generally their method is orthogonal to ours. We also include for comparison state-of-the-art dependency parsing results [START_REF] Bohnet | A transitionbased system for joint part-of-speech tagging and labeled non-projective dependency parsing[END_REF].

Conclusion

We presented an algorithm and a set of experiments showing that grammar extraction strategies can be combined in an elegant way and give state-of-the-art results when applied to high-quality phrase-based parsers. As well as repeating these experiments for languages which rely more on function annotation, we also plan to apply our method to other types of annotations, e.g. more linguistically motivated binarization strategies or -of particular interest to usannotation of empty elements.

  Figure 1: Binarization with markovization

Figure 3 :

 3 Figure 3: F1 for products of n grammars on the dev. set

7

  stp.lingfil.uu.se/ ˜nivre/research/Penn2Malt.

Table 1 :

 1 Parse evaluation on development set.

	Setting	F	EX
	No Func Right 92.26 42.97
	No Func Left	91.92 42.91
	Func Right	92.37 43.35
	Func Left	91.95 43.15
	DD Right Bin	92.71 44.44
	DD Left Bin	92.23 43.97
	DD Func	92.51 44.79
	DD No Func	92.52 44.08
	DD3	92.86 45.03
	DD4	92.82 45.14

Table 2 :

 2 Rate of certificates of optimality on the dev set.

	Setting	Rate
	DD Right Bin 99.24
	DD Left Bin	99.12
	DD Func	98.53
	DD No Func	99.12
	DD3	96.18
	DD4	94.53

Table 3 :

 3 Function labeling F1 on development set.

	Setting	SYSTEM FUN FUNTAG
	No Func Right	-	90.41
	No Func Left	-	90.26
	Func Right	89.61	90.37
	Func Left	89.29	90.40
	DD Right Bin	89.50	90.38
	DD Left Bin	89.11	90.31
	DD Func	89.54	90.49
	DD No Func	-	90.36
	DD3	89.48	90.42
	DD4	89.57	90.45

Table 4 :

 4 Dependency accuracies on the dev set

	Setting	Stanford		LTH p2m
		LAS	UAS	LAS	UAS UAS
	Func Right	92.18 94.32 89.51 93.92	94.2
	No Func Right 92.03 94.47 65.31 92.22	94.2
	Func Left	91.86 94.06 89.28 93.75	93.9
	No Func Left	91.83 94.29 65.33 92.18	94.1
	DD Right Bin	92.56 94.60 89.81 94.17	94.5
	DD Left Bin	92.01 94.38 89.62 94.05	94.2
	DD Func	92.19 94.36 89.67 94.06	94.2
	DD No Func	92.19 94.57 65.44 92.37	94.3
	DD3	92.77 94.79 90.04 94.33	94.5
	DD4	92.59 94.62 89.95 94.24	94.4

Table 5 :

 5 Test Set Results: Parseval F-score, penn2malt UAS, Function Label Accuracy and Funtag Function Label Accuracy are shown in Table 6.

	Comparison	Dev Test
	Func Right vs. No Func Right	✗	✗
	Func Left vs. No Func Left	✗	✗
	Func Right vs. Func Left		✗
	No Func Right vs. No Func Left	✗	✗
	DD Right Bin vs. Func Right
	DD Right Bin vs. No Func Right
	DD Left Bin vs. Func Left
	DD Left Bin vs. No Func Left
	DD Right Bin vs DD Left Bin
	DD Func vs. Func Right	✗
	DD Func vs. Func Left
	DD No Func vs. No Func Right
	DD No Func vs. No Func Left
	DD Func vs. DD No Func	✗	✗
	DD3 vs. DD Right Bin	✗
	DD3 vs. No Func Left
	DD3 vs. DD Func
	DD4 vs. DD. Right Bin	✗
	DD4 vs. DD. Left Bin
	DD4 vs. DD Func
	DD4 vs. DD3	✗	✗

Table 6 :

 6 Statistical Significance Testing

For brevity and without loss of generality, we omit unary and n-ary rules, as PCFG-LA admit a Chomsky normal form.

We denote the parse forest of a sentence by F and the characteristic function of a set by 1.

The anchor s of a label is composed of the span (i, j), denoting that the label covers terminals of the input sentence from index i to index j. In case the grammar contains unary nonlexical rules, the anchor also discriminates the different positions in a sequence of unary rules.

The LORG parser is available at https://github. com/CNGLdlab/LORG-Release and the modification at https://github.com/jihelhere/LORG-Release/ tree/functional_c11.

Their other system relying on the self-trained version of the BLLIP parser achieves 92.6 F1.

Acknowledgments

We are grateful to the reviewers for their helpful comments. We also thank Joachim Wagner for providing feedback on an early version of the paper. This work has been partially funded by the Labex EFL (ANR/CGI).


Marta K Schütz

Rebeca Leite De

Souza Moreira

Olivier Bildstein

Jean-Eric Lartigue

Michel L Schlegel

Bernard Tribollet

Vincent Vivier

Marie Libert

Rebeca Leite

Rebeca Moreira

Combined geochemical and electrochemical methodology to quantify

Keywords: biocorrosion, iron-reducing bacteria, dihydrogen, SEM micrographs, Raman microspectroscopy, chronoamperometry

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Disposal of high-level nuclear waste (HLW) in deep geological repositories is increasingly considered as a reliable solution in many countries. In France, for example, the current option explored is to store the vitrified HLW in stainless steel containers, conditioned in carbon steel overpacks which are then emplaced in a deep underground repository (about 500 m deep) in an argillaceous formation (claystone). This is known as a multi-barrier system, designed to ensure long-term radionuclide confinement. One of the purposes of the multibarrier system is to prevent water circulation around the metallic packages, thus preventing corrosion in water-saturated conditions.

However, knowledge about steel corrosion processes, especially over a long time period, must still be expanded to ensure that geological disposals will remain safe over a period of several hundreds of thousand years. The main issues related to steel corrosion are the influences of physico-chemical conditions (e.g. water saturation, pressure, temperature, pH, redox potential), and consequently microbial activity, on the durability of the different metallic packages.

Several studies reveal the presence of microorganisms in most of the deep clay formations already investigated, such as Callovo-Oxfordian argillite and Opalinus clay [START_REF] Stroes-Gascoyne | Microbial analysis of samples from the tunnel sealing experiment at AECL's Underground Research Laboratory[END_REF][START_REF] Poulain | Microbial investigation of Opalinus Clay, an argillaceous formation under evaluation as a potential host rock for a radioactive waste repository[END_REF]. Therefore, an impact of the microbial activity can be expected with respect to the various phenomena that may occur within the repository, such as (i) radionuclide migration through clay formations (including effects of biofilms); (ii) build-up of the gas phase by microbial gas production; and (iii) Microbiologically Influenced Corrosion (MIC) or biocorrosion [START_REF] Keith-Roach | Microbial interactions with radionuclides -summary and future perspectives[END_REF][START_REF] Stroes-Gascoyne | An overview of microbial research related to high-level nuclear waste disposal with emphasis on the canadian concept for the disposal of nuclear fuel waste[END_REF] which is discussed in this study.

Energetic compounds and nutrients are available to support microbial activity under geological conditions. Nutrients may be present either as soluble species in the groundwater or in minerals (solid-associated forms). Among the energetic compounds, H2 is expected to be one of the most efficient substrates (acting as an electron donor) [START_REF] Lin | The yield and isotopic composition of radiolytic H2, a potential energy source for the deep subsurface biosphere[END_REF]. It can be produced by radiolytic dissociation of water or by anoxic aqueous metallic corrosion [START_REF] Galès | Molecular hydrogen from water radiolysis as an energy source for bacterial growth in a basin containing irradiating waste[END_REF][START_REF] Libert | Molecular hydrogen: An abundant energy source for bacterial activity in nuclear waste repositories[END_REF]. Moreover, Fe(III) from clay minerals [START_REF] Kostka | Reduction of structural Fe(III) in smectite by a pure culture of Shewanella putrefaciens strain MR-1[END_REF][START_REF] Kostka | The impact of structural Fe(III) reduction by bacteria on the surface chemistry of smectite clay minerals[END_REF] and corrosion products, such as magnetite (Fe3O4) [START_REF] Kostka | Dissolution and Reduction of Magnetite by Bacteria[END_REF][START_REF] Schütz | Dissimilatory Iron Reduction in presence of Hydrogen: A case of Microbial Activity in the Nuclear Waste Disposal[END_REF][START_REF] Bildstein | Modelling iron-clay interactions in deep geological disposal conditions[END_REF][START_REF] Martin | Corrosion of iron and low alloyed steel within a water saturated brick of clay under anaerobic deep geological disposal conditions: An integrated experiment[END_REF][START_REF] Schlegel | Metal corrosion and argillite transformation at the water-satured, high temperature iron-clay interface: A microscopic-scale study[END_REF], could be a significant electron acceptor for anaerobic microbial respiration (by dissimilatory processes). The availability of such substrates may sustain the development of hydrogen-oxidizing bacteria (HOB) and iron-reducing bacteria (IRB), which in turn could have an impact on geochemical and corrosion processes in deep geological environments.

Several studies have dealt with the impact of sulfate-reducing bacteria (SRB) [START_REF] Rainha | Kinetic studies on the SRB influenced corrosion of steel: a first approach[END_REF][START_REF] Féron | Influence of microorganisms on the free corrosion potential of stainless steels in natural seawaters[END_REF][START_REF] Beech | Sulfate-reducing bacteria in biofilms on metallic materials and corrosion[END_REF][START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF] on corrosion processes. In contrast, the impact of IRB species has been only marginally investigated. Their role in biocorrosion is still under debate; either an inducing or an inhibitory effect by formation of a protective biofilm on metal surface have been hypothesized [START_REF] Dubiel | Microbial Iron Respiration Can Protect Steel from Corrosion[END_REF][START_REF] Lee | Microbial iron respiration: impacts on corrosion processes[END_REF][START_REF] Herrera | Role of iron-reducing bacteria in corrosion and protection of carbon steel[END_REF]. Recent studies have investigated the impact of IRB on metallic corrosion processes under geological disposal conditions [START_REF] Esnault | Metallic corrosion processes reactivation sustained by iron-reducing bacteria: Implication on long-term stability of protective layers[END_REF][START_REF] Libert | Biocorrosion en conditions de stockage géologique de déchets radioactifs[END_REF][START_REF] Moreira | Local Electrochemical Measurements Applied to Biocorrosion[END_REF]. IRB species can use Fe(III) from magnetite or other Fe(III) (hydr)oxides as electron acceptor in the presence of H2 as electron donor. An alteration of the (hydr)oxide layers with a possible reactivation of the corrosion process may thus occur as a consequence of the Fe(III) bacterial respiration [START_REF] Esnault | Metallic corrosion processes reactivation sustained by iron-reducing bacteria: Implication on long-term stability of protective layers[END_REF].

This study investigates the effect of the HOB and IRB activities on the corrosion rate of carbon steel in the presence of H2 as the sole electron donor. These investigations are supported by geochemical and electrochemical techniques. Geochemical analysis allows the monitoring of the metal dissolution and the formation of Fe(II,III) solid corrosion products during the bacterial oxidation of H2 produced by corrosion. Local electrochemical techniques allow to generate a high H2 concentration for bacterial metabolism and then to probe the bacterial reaction in terms of modification of the local potential.

Materials and methods

Bacterial culture

Shewanella oneidensis strain MR-1 (ATCC 700550 TM ) was chosen as a model of IRB and HOB. Cultures were obtained aerobically at the beginning of stationary growth phase in Luria Bertani Broth (LB) medium (5 g L -1 NaCl, 10 g L -1 tryptone, 5 g L -1 yeast extract) after 24 h at 30°C under sterile conditions. Bacterial cells were harvested from the LB medium by centrifugation (4000 rpm for 20 min), washed once with sterile minimal medium (M1) and then inoculated in the batch reactors (initial concentration 10 8 cells mL -1 counted by epifluorescence method with LIVE/DEAD ® BacLight™ kit). The chemically defined minimal medium (M1) was prepared according to [START_REF] Kostka | Isolation, cultivation, and characterization of iron-and manganese-reducing bacteria[END_REF] [START_REF] Kostka | Isolation, cultivation, and characterization of iron-and manganese-reducing bacteria[END_REF]. However, minor modifications were made to the composition [START_REF] Esnault | Metallic corrosion processes reactivation sustained by iron-reducing bacteria: Implication on long-term stability of protective layers[END_REF] in order to obtain a representative solution of the groundwater found in the argillaceous formations for geological disposal in France. The final composition is shown in Table 1.

Here Table 1 The pH was adjusted to ca. 7 with NaOH and then the medium was sterilized by autoclaving (120°C for 20 min), except for the thermolabile components (e.g. amino acids) which were filter-sterilized (0.22 µm) and added to the autoclaved medium.

Carbon steel coupons

Corrosion studies were performed with low carbon steel coupons A37 supplied by the French Alternative Energies and Atomic Energy Commission (CEA). They contain 0.12% C, 0.22% Si, 0.62% Mn, 0.008% Al, 0.012% S, 0.012% P, 0.02% Ni, 0.03% Cr, 0.04% Cu, 0.005% Co and <0.005% Ti. Carbon steel is a corrosion-allowance material which is expected to have nearly-uniform corrosion in a reducing environment, and has been therefore considered as a candidate material for packages used in the geological disposal.

The cylindrical coupons were laterally insulated from the solution by a diallylphthalate glass-fiber resin (Presi) in order to expose only an active surface of 0.78 cm 2 . Then, the coupons were polished with 600 grit SiC abrasive paper and sterilized with ethanol by sonication for 15 min prior to the experiments.

Batch experiments

All experiments started under strictly sterile conditions in batch reactors at 30 o C under an anaerobic atmosphere. Both abiotic and biotic conditions were investigated.

Geochemical techniques

The geochemical experiments were performed in triplicate in 140 mL of M1 medium under N2/CO2 (90:10%) atmosphere. The corrosion reaction was monitored as a function of time by gas and solution analyses. The aqueous Fe concentration was analyzed by Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES, Varian, VISTA-MPX) after 0.02 µm filtration and 2% (v/v) HNO3 acidification. The analysis of H2 in the headspace was carried out by Micro Gas Chromatography (Varian, CP-4900) using a thermal conductivity detector with N2 as carrier gas. The total H2 concentration was calculated as the sum of the concentrations in the gas and the aqueous phases (determined using Henry's law).

Electrochemical techniques

The electrochemical measurements were performed with a home-made Scanning Electrochemical Microscope (SECM) [START_REF] Gabrielli | A SECM assisted EQCM study of iron pitting[END_REF][START_REF] Keddam | Progress in Scanning Electrochemical Microscopy by Coupling with Electrochemical Impedance and Quartz Crystal Microbalance[END_REF] in a 4-electrode cell configuration elaborated specifically for anaerobic and sterile conditions. The double wall glass cell was equipped with the carbon steel working electrode (WE1) placed in the bottom of the cell, and with a platinum probe of 50 µm in radius acting as a second mobile working electrode (WE2) for generating H2. The cell was sealed with a Teflon cover and the platinum WE2 probe was placed through a nitrile flexible support on the cover, perpendicular to WE1, in a way to allow its displacement for the measurements. The WE2 microelectrode was positioned with the help of motorized stages driven by a motion controller (Newport) with Labview software. Both working electrodes used as reference a saturated calomel electrode (SCE) and a platinum grid as counter electrode.

The disassembled cell and the platinum WE2 probe were sterilized prior to the experiments with 70% ethanol solution for 20 min; then rinsed with sterilized water in a laminar flow chamber and finally UV-irradiated for 15 min. The lugging capillary (for holding the reference electrode) and the platinum grid counter electrode were sterilized in autoclave. The cell was assembled under sterile conditions and 230 mL of M1 medium was introduced and deaerated for 2 h under N2 atmosphere. The N2 flow was maintained at the cell headspace (near to the liquid surface) so as to ensure the anaerobic conditions during the whole electrochemical measurements. A supplementary N2 bubbling of the bulk solution was also carried out during inoculation of the electrochemical cell.

An approach curve was performed at a rate of 7.5 µm s -1 with the probe polarized at -0.9 V/SCE and the substrate held at Open Circuit Potential (OCP). Such approach curve allowed the contact point between the steel substrate and the apex of the probe to be determined with a spatial resolution better than a fraction of micrometer. Then, the microelectrode was repositioned at 50 µm from the substrate and polarized for generating locally H2 (Scheme 1). The use of SECM for generation or collection of H2 in solution has already been described in the literature [START_REF] Nicholson | Electrocatalytic activity mapping of model fuel cell catalyst films using scanning electrochemical microscopy[END_REF][START_REF] Trinh | Alternating Current Measurements in Scanning Electrochemical Microscopy, Part 2: Detection of Adsorbates[END_REF].

Here Scheme 1

Characterization of the coupon surface

Steel coupon surfaces in the geochemical experiments were analyzed, after 5 months of reaction, by Raman microspectroscopy and Scanning Electron Microscopy (SEM). The coupon surfaces of the electrochemical experiments were analyzed only by SEM. The samples for the Raman analysis were kept in anoxic containers and the measurements were performed through a glass plate (500 µm thick) using a LabRam HR (Horiba Jobin Yvon) spectrometer equipped with a 532 nm laser and a 50x long range lens. The laser power was 50 mW attenuated by a factor of 100. The acquisition time ranged from 60 to 600 s depending on the spectral quality. The Raman spectra are presented in this study without smoothing or line fitting. The spectra analysis was performed by comparing the significant bands with literature data [START_REF] Faria | Raman Microspectroscopy of Some Iron Oxides and Oxyhydroxides[END_REF][START_REF] Hanesch | Raman spectroscopy of iron oxides and (oxy)hydroxides at low laser power and possible applications in environmental magnetic studies[END_REF][START_REF] Bellot-Gurlet | Raman studies of corrosion layers formed on archaeological irons in various media[END_REF][START_REF] Frost | Raman and infrared spectroscopic study of the vivianite-group phosphates vivianite, baricite and bobierrite[END_REF][START_REF] Frost | Raman spectroscopic study of vivianites of different origins[END_REF]. SEM studies were performed at 20 keV and 5.3 nA with a Leica Stereoscan 440 microscope coupled with Energy Dispersive Spectroscopy (EDS) for elemental semi-quantitative analyses (Princeton Gamma-Tech). The samples were slightly rinsed with deionised water, dried with N2 gas and stored in plastic containers until analysis. The coupons were carbon coated prior to SEM analysis.

Results and discussion

Geochemical results

Under anaerobic conditions, carbon steel corrosion (simplified as Fe in the Eqs. 1 & 3) is described by iron oxidation as the anodic reaction (Eq. 1) and water reduction as the cathodic reaction (Eq. 2):

Fe → Fe 2+ + 2 e - (1)
2H2O + 2e -→ 2HO -+ H2

According to the overall reaction (Eq. 3), the molecular stoichiometry of Fe:H2 produced by corrosion is 1:1:

Fe + 2H2O → Fe 2+ + 2OH -+ H2 (3)
Figure 1 shows the evolution of Fe and H2 produced by carbon steel corrosion.

Here Fig. 1 In abiotic conditions, equimolar H2 and dissolved Fe are released, which is in good agreement with the stoichiometry of the Eq. ( 3). Effective biocorrosion was evidenced by the larger amounts of Fe and H2 produced at about 5 days compared to abiotic conditions. Moreover, in presence of bacteria, H2 concentration remains much lower when compared to dissolved Fe concentration. Such evidence suggests that bacteria consume the soluble H2 in the aqueous phase for respiration. Several studies have indeed shown that H2 is an important energetic substrate, especially in disposal environments where only low amounts of biodegradable organic matter are available [START_REF] Lin | The yield and isotopic composition of radiolytic H2, a potential energy source for the deep subsurface biosphere[END_REF][START_REF] Libert | Molecular hydrogen: An abundant energy source for bacterial activity in nuclear waste repositories[END_REF][START_REF] Chapelle | A hydrogen-based subsurface microbial community dominated by methanogens[END_REF].

The pH in the bulk solution was initially equal to 6.47 and only a slight increase was observed at the end of the experiments for both abiotic and biotic conditions, with values of 6.54 and 6.62, respectively (data not shown).

A black layer and a white precipitate (over the black layer) were progressively formed on the coupon surface in both abiotic and biotic conditions, suggesting a reaction between the surface and species in solution which also resulted in a decrease in the aqueous Fe concentration after 20 days of reaction (results not shown in Figure 1). The Raman analysis for the solid corrosion products formed in abiotic conditions (Figure 2a) revealed the presence of vivianite (Fe3(PO4)2.8H2O) (i & iii) and magnetite (ii) as the most abundant mineral phases. In contrast, for the biotic conditions (Figure 2b), the intensity of vivianite bands is greater (i & iii); the intensity of magnetite band significantly decreases (ii); and relatively intense bands appear in the region 1440 cm -1 (iv), which may indicate cellular compounds (e.g. lipids, enzymes like hydrogenase) on the coupon surface. The magnetite band is broad, suggesting formation of a mineral phase with poor crystallinity.

Here Fig. 2 The SEM analysis also revealed vivianite as corrosion product for both abiotic (Figures 3a &b) and biotic (Figures 3e &f) conditions. A modification in the morphology of this mineral was observed in the presence of bacteria. Moreover, in biotic conditions the black layer morphology and chemical composition are modified (Figures 3g &h), compared to those in abiotic conditions (Figures 3c &d). Both Raman and SEM analyses point out a modification of the composition and crystallinity of corrosion products by the bacterial activity.

The literature proposes different mechanisms of bacterial-induced corrosion. Widdel's group have hypothesized that, in the case of SRB and methanogenic species, corrosion is enhanced by direct electron transfer from metal to bacterial cells [START_REF] Venzlaff | Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria[END_REF][START_REF] Dinh | Iron corrosion by novel anaerobic microorganisms[END_REF]. In contrast, we can assume that, in the case of IRB species, dissimilatory reduction of Fe(III) promotes the solubilization and removal of (hydr)oxide layers, exposing carbon steel surfaces to corrosion [START_REF] Herrera | Role of iron-reducing bacteria in corrosion and protection of carbon steel[END_REF][START_REF] Esnault | Metallic corrosion processes reactivation sustained by iron-reducing bacteria: Implication on long-term stability of protective layers[END_REF]. To date, direct contact, nanowires and electron shuttling have been proposed as strategies for dissimilatory Fe(III) reduction from insoluble substrates [START_REF] Luu | Review: microbial mechanisms of accessing insoluble Fe(III) as an energy source[END_REF]. Our results corroborate these findings, showing that Shewanella oneidensis can reduce Fe(III) from magnetite using soluble H2 produced during the corrosion process as an electron donor.

Here Fig. 3

Electrochemical results

Figure 4 shows the OCP variation of the carbon steel electrode in the M1 solution. Such measurement indicates the variation of the difference of potential between the carbon steel working electrode and the reference electrodes at the equilibrium state over time. The OCP remains stable at -714 mV/SCE during the first 16 h of the experiment. Then, the supplementary N2 bubbling of the solution for 1 h is accompanied by a small decrease of the potential (about 23 mV). The OCP is slightly perturbed upon addition of the Shewanella oneidensis inoculum, but then it slightly decreases and stabilizes at ca. -718 mV/SCE after a few hours.

Here Fig. 4 After mapping experiments (data not shown), in which the platinum probe was polarized to generate H2, we noticed a formation of solid phases over the entire surface of the steel substrate (Figure 5a). SEM micrograph of the substrate at the position where the H2 was locally generated (target area in Figure 5a) is shown in Figure 5b. A more important mineralization was observed on this specific area, in the vicinity of the probe, where H2 was kept in a confinement volume (ca. 3.9 x 10 -8 cm 3 ). This observation suggests an influence of the corrosion increase in this localized area. Changes in the local pH, redox potential, or even the enhancement of the bacterial activity due to a greater availability of energetic substrate (H2) can be considered as potential factors for the mineralization effect. The EDS analysis of a single crystal (Figures 5d &c, respectively) shows the formation of iron phosphate as vivianite.

Here Fig. 5 During the corrosion process two phenomena take place simultaneously -the anodic reaction (Eq. 1) and the cathodic reaction (Eq. 2). At the equilibrium (OCP), the net current in the substrate is zero. When the potential of the steel electrode is set to a value greater than the OCP, the anodic dissolution of the substrate is favored. We thus biased the substrate state in order to control the kinetics of dissolution and we locally generated H2 through the probe brought to the vicinity of the substrate. The distance between the steel substrate and the probe was set at 50 µm by performing a preliminary approach curve [START_REF] Kwak | Scanning electrochemical microscopy. Theory of the feedback mode[END_REF]. With such a device (sketched in Scheme 1), it was possible to reproduce and to control the different processes that usually take place simultaneously on the steel electrode.

The steel dissolution was monitored over 5 days for different corrosion conditions by measuring the total current of the electrode in order to reveal the influence of the local H2 concentration (Figure 6). The corrosion rate was shown to depend on the presence of both bacteria and the H2 generated. When the potential of the steel electrode is biased at OCP, in the abiotic conditions and without H2 generation (Figure 6, curve a), the current remains in the range of 0.5 µA cm -2 . In contrast, when H2 is generated, the current of the steel electrode increases to about 1 µA cm -2 and remains in a quasi steady-state regime (Figure 6, curve b). The positive feedback regime that takes place between the probe and the substrate explains this behavior [START_REF] Kwak | Scanning electrochemical microscopy. Theory of the feedback mode[END_REF]. In biotic conditions, a steady increase of the current is observed during the 5 days (Figure 6, curve c).

Here Fig. 6 The integration of the anodic current of each experiment provides the exchanged charge during the corrosion process (Table 2). These results clearly indicate that in biotic conditions and with local H2 generation, the corrosion magnitude is significantly increased due to an increase of the bacterial activity (the more dihydrogen is produced, the more the consumption of iron by the bacteria). It is noteworthy that these experiments do not allow the measurements of the H2 produced by the corrosion process, only the H2 generated by the probe.

Here Table 2 Again, the carbon steel surface exhibited a mineralization as iron phosphate. It should also be mentioned that longer experiments (more than 5 days) are usually difficult to perform in such experimental conditions, since the distance between the probe and the substrate is small (50 µm) so as to confine the H2 generation. Hence, the biocorrosion can lead to accumulation of corrosion or biological products between the probe and the substrate. Bacterial adhesion on the carbon steel surface can also be observed after the experiments, as shown in Figure 7, which is an another indication of the bacterial action on the corrosion process.

Here Fig. 7 3

.3. Corrosion rate results

The corrosion rates were obtained from the results of the geochemical and electrochemical experiments. In the case of geochemical measurements, the corrosion rate was estimated from the aqueous Fe concentration (shown in Figure 1), according to Eq. ( 3) and assuming no precipitation of corrosion products during the first 20 days of reaction. In contrast, in the case of electrochemical measurements, the charges for steel corrosion obtained for 5 days were converted considering the general value for steel (j = 86.3 µA cm -2 equal a corrosion rate of 1 mm year -1 ) [START_REF] Lemaitre | Biodétérioration des matériaux[END_REF].

Figure 8 and Table 2 show the corrosion rates obtained from the geochemical and electrochemical results, respectively. Figure 8 shows that the short-term corrosion rate is higher than the long-term one for both abiotic and biotic conditions. The bacterial effect on the corrosion rate tends to decrease with time, suggesting a depletion of nutrients because of experimental conditions (batch reactors) leading to a limitation of bacterial development. Average rates are estimated at 100 µm year -1 and 30 µm year -1 for biotic and abiotic conditions, respectively, after a period of about 20 days.

Here Fig. 8 The corrosion rates obtained by the electrochemical results (Table 2) show values that are significantly smaller when compared to the geochemical results because of the choice of the potential applied for the measurements. At OCP, anodic and cathodic currents are contributing to the overall reaction and, in this case, the cathodic reaction (water reduction) is not taken into account and the anodic current (steel dissolution) value is therefore underestimated. Although the corrosion rate values obtained in the electrochemical and geochemical experiments cannot be directly compared, they demonstrate a clear influence of the bacterial activity. The corrosion rates are shown to be greater in biotic than abiotic conditions with both techniques.

Conclusions

Safe disposal of HLW is a key issue of waste management. The current disposal concept relies on a multi-barrier system which includes different metallic packages (stainless steel, carbon steel). Over time, production of H2 and Fe(II,III) solid corrosion products is expected due to the anoxic aqueous corrosion. Such corrosion products can provide respiratory substrates for bacterial activities. Therefore, the influence of the biological parameter on corrosion has to be also evaluated in order to demonstrate the safety of the disposal system.

This study demonstrates that the corrosion process is enhanced by a factor of 2-3 in presence of bacteria. The geochemical results showed that after 5 days a greater amount of Fe and H2 is produced during corrosion in comparison with abiotic conditions. Moreover, the consumption of the soluble H2 in the aqueous phase by bacteria is evidenced as well as a modification in the composition and crystallinity of the solid corrosion products (magnetite and vivianite) on the carbon steel surface. Still, the electrochemical results showed a higher mineralization (vivianite) and corrosion rate in presence of bacteria when H2 is generated in a small confinement volume (ca. 3.9 x 10 -8 cm 3 ). So, our results suggest that Shewanella oneidensis likely induces corrosion by reduction of Fe(III) from magnetite using soluble H2 produced by the corrosion process as electron donor.

However, it remains to be determined if the bacterial activity will have a similar longterm effect on the corrosion rate under disposal conditions. A modeling approach, including calibrated parameters according to the results of the short-term experiments, could be used to extrapolate the corrosion kinetics and predict biocorrosion processes on a long-term scale. the supervision of Dr. L.T. Yu in Thiais (France). In 2002, he joined the Laboratoire Interfaces et Systèmes Électrochimiques (CNRS -UPR 15). His current research field concerns the characterization of heterogeneous interface reactivity by means of local electrochemical techniques and electrochemical impedance spectroscopy. Marie Libert received her PhD in biochemistry (1986) from the University of Compiegne-France. She is a senior research engineer at the French Commission for Atomic Energy and Alternative Energies (CEA) since 1998. Her previous affiliation includes a doctoral fellowship at the same university. Her research focuses on different fields such as the effect of microorganisms on long term behaviour of materials used in nuclear repository, biocorrosion, impact of radioactive emission on biota, anaerobic microbiology. She was and she is an European expert on several international research programs. 6) with the respective corrosion rates.

Figure 1 :

 1 Figure 1: Production of Fe and H2 by carbon steel corrosion during the geochemical experiments (n=3): Fe ( , ) and H2 ( , ) concentrations (µM) as function of time (days). Biotic conditions ( , ) and abiotic conditions ( , ).

Figure 2 :

 2 Figure 2: Raman spectra of corrosion products detected on steel coupons reacted during 5 months in the geochemical experiments. (a) Abiotic conditions: vivianite (i) and (iii); magnetite (ii). (b) Biotic conditions: vivianite (i) and (iii); magnetite (ii); and cellular compounds (iv). Each spectrum in the figures is representative of the signal collected on the sample surface.

Figure 3 :

 3 Figure 3: SEM micrographs and EDS spectra of corrosion products formed by carbon steel corrosion after 5 months in the geochemical experiments. (a-d) Abiotic conditions: precipitate formed over the black layer (a, b) and black layer (c, d). (e-h) Biotic conditions: precipitate formed over the black layer (e, f) and black layer (g, h). The rectangle on SEM images corresponds to the areas analyzed by EDS.

Figure 4 :

 4 Figure 4: Evolution of the OCP (V vs. SCE) as function of time (hours) of the carbon steel substrate before and after inoculation of Shewanella oneidensis during the electrochemical experiments.

Figure 5 :

 5 Figure 5: SEM micrographs of carbon steel coupon reacted during 3 days in biotic conditions in the electrochemical experiments. (a) Global view of the coupon surface. (b) View of the center where the H2 generating probe was placed. (c) View of a single crystal formed. (d) EDS spectrum of the crystal shown in Figure c.

Figure 6 :

 6 Figure 6: Chronoamperometric response (µA cm -2 ) as function of time (hours) of the carbon steel substrate in biotic conditions for electrochemical experiments. (a) No local H2 generation by the probe. (b) Without Shewanella oneidensis under a local H2 generation by the probe. (c) With both Shewanella oneidensis and local H2 generation by the probe.

Figure 7 :

 7 Figure 7: SEM micrograph showing attachment of bacteria on the carbon steel surface after 10 days in the electrochemical experiments. The rectangle on SEM images indicates the cells of Shewanella oneidensis. No fixation treatment was performed for the analysis.

Figure 8 :

 8 Figure 8: Corrosion rate (µm year -1 ) as function of time (days) measured at the outset of the geochemical experiments (n=3): biotic ( ); and abiotic ( ) conditions.

FIGURE 1 FIGURE 2 21

 12 FIGURE 1

FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 FIGURE 8

 345678 FIGURE 3

Table Captions Table 1 :

 Captions1 M1 minimal medium composition.

Table 2 :

 2 Determination of the exchanged charge (in millicoulomb) during the corrosion in different conditions (calculated from results presented in Figure

Acknowledgements

The authors thank Damien Féron (CEA Saclay, France) for carbon steel samples, Paul Soreau (IBEB, CEA Cadarache, France) for ICP-OES analysis and Françoise Pillier (LISE, UPR15, France) for SEM analysis. This research has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 238579 by the BIOCOR ITN project (website: www.biocor.eu/).

Author CVs

Marta Kerber Schütz received a BS degree in Industrial Chemistry from Catholic University of Rio Grande do Sul, Porto Alegre, Brazil in 2007; completed her MSc in Materials Science and Engineering in March 2010 at the same University. Now she is a PhD student at the French Commission for Atomic Energy and Alternative Energies (CEA). She is working on biocorrosion phenomena implicated on the radioactive waste geological disposal. The overall objective of her study is to better understand the impact of bacterial activities (notably IRB species) on the corrosion products (dihydrogen and iron (hydr)oxides) and on the rate of anoxic corrosion. (1994)(1995)(1996)(1997)(1998) and a position as hydrogeologist at the French Geological Survey (BRGM) (1993). His research focuses on numerical modeling of reactive, multicomponent, and multiphase flow and transport with application to long term evolution of materials in radioactive waste disposal, subsurface pollution/remediation, and potential bacteria mediated processes.

Rebeca

Jean-Eric


Molecular Rectification in Oriented Polymer Structures""

By Carole Sentein, * CCline Fiorini, Andrk Lorin, and Jean-Michel Nunzi Polymeric semiconductor devices are receiving increasing attention in view of potential applications requiring lowcost processing over large areas.'"*] In this respect, unlike with evaporated molecules, the wet-processing capability of polymers offers total compatibility with other complementary technologies. The concepts from which organic-semiconductor devices are designed are mostly derived from inorganic-semiconductor physics and technology. ''] In order to build efficient organic-semiconductor devices such as electroluminescent or photovoltaic solar cells, a rectifying junction is required. Such junction can be of two main typed4] Schottky junctions between an organic semiconductor and a metal, and p-n junctions between two pand n-type organic-semiconductors. The Schottky junctions often suffer from degradation problems originating from electrochemical potential differences at the rectifying contacts, which induce diffusion of electrode material into the polymer.'" Such a drawback is corrected with p-n junctions in which metal to polymer contacts are ohmic. However, p-n junctions require the use of two polymer layers with wet-processing compatibility. Moreover n-type organicsemiconductors are less common than p-type ones owing to their lower stability under oxygen which is a consequence of their reductive behavior.

We report here a different approach in which oriented diode-like molecules, the so-called push-pull molecules used in nonlinear optics, [START_REF] Bosshard | I? Giinter[END_REF] are contained inside a polymer binder. Oriented molecules induce a rectifying effect, behaving as a distributed homojunction within a single polymer thin film. In order to demonstrate the principle, we start with an initially symmetric structure: the polymer film is sandwiched between two identical electrodes. The current-voltage characteristics of the device are also symmetrical. By application of a static electric field through the polymer film, while heating near the glass transition temperature (T,,) dopant molecules are oriented in the field with an order parameter (cosO).['] The current-voltage characteristics then become strongly asymmetric.

Experimentally, molecular order is controlled using second harmonic generation (SHG): it appears that SHG-in- tensity is related to the induced rectification behavior. The principle we demonstrate relies on the intrinsic polar nature of organic molecules. It cannot be readily applied to inorganic semiconductors which are built from spherical atoms; polarity being a crystal-cell property. Time of flight (TOF) experiments reveal an unipolar increase of the electron mobility through orientation, thus confirming the molecular-diode organization effect. This new type of junction is expected to improve significantly the efficiency of polymeric semiconductor devices.

Figure 1 presents the current-voltage characteristics of the symmetric-electrode device monitored before and after orientation under different strengths of orientationfield. The rectifying effect induced by molecular orientation in the symmetric-electrode device is clearly seen in Figure 1, for orientation voltages larger than 10 V. It corresponds to an orientation field close to 100 V/pm. The insert in a logarithmic scale clearly shows that there is no initial rectification in the non-oriented device. The same effect was observed using symmetric-IT0 electrodes instead of aluminum. This proves that rectification is not due to some interfacial effect occurring between polymer and electrodes, such as aluminum oxidation.

In contrast, no rectification is induced using a single PVK-polymer film. This proves that rectification is not related to charge trapping effects. N o more rectification is induced in a 30 wt.-% non-polar phthalocyanine-PMMA blend. On the other hand, we replaced Disperse Red (DR1) by N-dibutyl-4-amino-4'-nitrostilbene (DBANS), another push-pull polar molecule, in a PVK-polymer blend. The induced rectification is then qualitatively the same as lor DR1. This proves that internal rectification is typical of the orientation of polar molecules.

ADVANCED MATERIALS

The positive part of the current-voltage curves can be fitted using standard charge injection models.[31 In order to estimate the rectification behavior, we chose the Schottky diode model which describes successfully the vast majority of single layer organic-semiconductor devices probed under fields up to around 100 V/pm,Ly,'"l where I is the measured current, I , the saturation current, V the applied field, n the so-called ideality factor, q the electron charge, k the Boltzmann constant and T the absolute temperature.

I = I, exp -- [ ($TI -I ]
For each device orientation-field value, we get the saturation current. Using the usual analogy with inorganic semiconductor^,^^^ we then calculate the equivalent barrier height @b between metal and polymer in the frame of the thermionic emission model, where A is the diode area and R* is the so-called Richardson constant usually approximated to its free electron value of 120 A cm-' K -~.

I, = AR*T2exp ~ (-3
In order to get a measurement of the molecular order (cosH) the average polar orientation along the field direction, we performed second-harmonic generation experiments.['] Initially, polar molecules are distributed isotropically, the material is centrosymmetric, and no SHG signal is detected. During the orientation step, we monitored the increase of the SHG signal, which is proportional to the square of the molecular order (cosfl) (insert in Fig. 2).'"71 SHG-monitoring permits optimization of the sample orientation parameters, i.e., orientation field, sample tempera- ture, poling duration, and cooling conditions, in order to achieve the largest stable orientation. Experiments were performed using a picosecond Nd:YAG laser. Using the same symmetrical device (Al/ DR1-MMA-50150 copolymeriAl) as the one used for the determination of the current-voltage characteristics in Figure 1, SHG was measured for each orientation field value. SHG was monitored before and after I-V-characteristic recording, without any change, indicating that molecular order is frozen despite the large fields achieved. Moreover, we performed SHG at ambient temperature in fields up to 220 V/pm, without any permanent SHG variation.

The relationship between the equivalent barrier height ds, and molecular order (cod) is shown in Figure 2. Through molecular orientation, we achieve a 0.2 eV reduction in the equivalent barrier height. @b, which is a measure of the induced internal rectification, exhibits a quasi-linear experimental dependence with molecular order. This phenomenological dependence may be attributed to the storage of an internal polarization field proportional to (cos8).

Together with the asymmetry of the I-V curve induced upon orientation in Figure 1, molecular-diode organization may affect charge mobility. In order to address this point, we performed time of flight (TOF) experiments.

["] Samples used for TOF were 1.5 Fm-thick films sandwiched between a transparent ITO-electrode and an Al-electrode. A typical TOF transient obtained with the strongly absorbed frequency-doubled output of a pulsed Nd:YAG-laser is given in the insert of Figure 3. Majority carriers in the DR1-

/'- / ' aio-71 K ' 0 . 7 ~1 0 ~ 0 . 9 ~1 0 ~ 1.1~1 o3
El" (V/cm)1'2 MMA-50150 copolymer appear experimentally to be electrons. Field-dependence of the electron drift-mobility is given in Figure 3, before orientation and after orientation with two opposite orientation-field values. The mobility exhibits a Poole-Frenkel-type field dependence." '] The increase of the electron mobility is significant when molecules are oriented under reverse bias with respect to ADVANCED Communications the measurement field; that is to say with the acceptor group oriented towards the Al-electrode. On the other hand, mobility is weakly changed when molecules are oriented under direct bias. By extrapolation to its zero-field limit using the Poole-Frenkel dependence, mobility in the sample oriented under reverse bias is increased by a factor of 4 with respect to the unoriented sample. According to Figure 2, the internal field resulting from molecular orientation is close to 2 Vipm (A@, = 0.2eV in a 130 nm thick device): it is negligible compared to the field applied for mobility measurements (Fig. 3). As a consequence, unipolar enhancement of the mobility reveals the moleculardiode organization effect through orientation.

In conclusion, we have given experimental evidence for molecular rectification in an oriented amorphous polymer incorporating polar chromophores. Rectification implies storage of an internal field, thus reducing potential barriers for charge injection or extraction at both electrodes. Reduction of potential barriers may slow down oxidation-reduction reactions occurring spontaneously at non-ohmic metal-polymer junctions, thus slowing down device degradation. Additionally, using engineered asymmetric electrodes, this rectification effect may improve significantly the efficiency of polymeric semiconductor devices such as photovoltaic cells and electroluminescent diodes. Polar organization of molecular diodes is equivalent to the build-up of a distributed p-n homojunction within a single polymer film. In addition to the ease of processing of such devices, our solution offers a crucial advantage over usual p-n junctions. The efficiency of organic-semiconductor p-n junction devices is usually limited by the weak extension of the depletion zone (typically 10 to 50 nm),[4J in which the majority of charge separation or recombination processes take place. Our solution provides a depletion zone extending over the whole polymer film thickness. Moreover, diodelike molecules orientation results in an enhancement of charge mobility. This may also improve organic-device efficiency which suffer from low charge mobilities.

The materials used in this study have not been optimized for device efficiency, but rather they were designed in order to demonstrate rectification induced through orientation of diode-like molecules. An optimization route with respect to long-term stability would consist in designing a high-T, semiconducting polymer. Additionally, the poling technique may be greatly improved by using the corona-poling techniqueL6] which permits the achievement of larger orientation orders over large areas. Experiments are now in progress to apply this principle to photovoltaic solar cells.

Experimental

As an active polar molecule, we used Disperse Red 1 (DR1): 4-(1\'-(2-hydroxyethyl)-N-ethyl)-amino-4'-nitroarobenLenc. It is a typical push-pull molecule with a donoritransmitterhcceptor structure and it possesses a large ground state dipole moment 1' which is necessary for efficient DC-field orientation. It is attached onto polymethylmethacrylate (PMMA) which is used as an isotropic polymer binder. The resulting copolymer DRI-MMA-SO150 contains 50 %-molar chromophore concentration [S]. Its glass transition temperature is Tg = 132°C.

Test devices were realized on top of standard glass slides. They consisted of a vacuum-evaporated 12 nm-semi-transparent aluminum bottom-electrode, covered by a 130 nm DR1-MMA-50150 copolymer film spin-coated from a 1,1,2-trichloroethane solution, and finally recovered by a second identical semi-transparent aluminum top-electrode. The active surface of the device was 26 mm'.

Orientation of the polar molecules was achieved by application of a 5 to 20 V voltage between the electrodes for 10 min while the device was heated at 130°C. The sample is then cooled down to room temperature with the voltage still applied, in order to freeze-in the molecular order. 80 % of the molecules remain oriented after more than two months. Owing L o the small polymer-film thickness, some samples prepared in this way initially exhibited short circuits. These short-circuits were readily cured during monitoring of the very first current-voltage characteristics. After curing, all the samples from the same batch gave identical and reproducible results. The preparation technique also was reproducible.

  [*] Dr. C. Sentein. Dr. C. Fiorini, Dr.A. Lorin, Dr. J.-M. Nunzi LET1 (CEA-Technologies Avancees) DEIN-SPE. Groupe Composants Organiqucs Centre d'Etudes de Saclay, F-91191 Gif-sur-Yvette (France) [**I This work was supported by the EEC under JOULE contract PL 950441. We thank Dr. Brigitte Mouanda for carrying oul DSC and thermal gravimetry experiments, and Dr. Paul Raimond for supplying the copolymer.

Fig 1 .

 1 Fig 1. Current-voltage characteristics of the AlicopolymeriAl symmetric device before and after orientation by different voltages. Data markers are used as a guide to the eye. The insert is the absolute value of measured current in a logarithmic scale. In the insert continuous lines show fits of the Schottky model for the positive parts of I-V curves.

Fig. 2 .

 2 Fig. 2. Variation of the cquivalent barrier height between Al and DR1-MMA-S0/50 copolymer with respect to the DR1-molecules orientation order in the PMMA matrix. Molecular order is given as the square root of SHG-signal. Barrier height Ob is deduced from current-voltage characteristics. Insert depicts SHG-growth with time at 130°C under different orientation-field values.

Fig. 3 .

 3 Fig. 3. Field dependence of the electron drift-mobility in thc DR1-MMA-SO/ 50 copolymer before orientation (open triangles), after direct orientation uiider 100 V (full squares). and after reverse orientation under -100 V (full circles). Insert depicts a typical TOF transient for the unoriented sample.

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1991, 9, No. 10