Thaïs Baudon

Carsten Fuhs

Laure Gonnord

Parallel Complexity of Term Rewriting Systems *

Keywords: 2012 ACM Subject Classification Theory of computation → Program verification, Rewrite systems; Software and its engineering → Automated static analysis, Formal software verification Complexity analysis, Parallelism, Rewriting 1

In this workshop paper, we revisit the notion of parallel-innermost term rewriting. We provide a definition of parallel complexity and propose techniques to derive upper bounds on this complexity via the Dependency Tuple framework by Noschinski et al.

Introduction

In this paper, we consider the problem of evaluating the potentiality of parallelisation in pattern-matching based recursive functions like the one depicted in Figure 1. In this particular example, the recursive calls to left.size() and right.size() can be done in parallel. Building on previous work on parallel-innermost rewriting [START_REF] Vuillemin | Correct and optimal implementations of recursion in a simple programming language[END_REF][START_REF] Fernández | Orderings for innermost termination[END_REF], and first ideas about parallel complexity [START_REF] Alias | Estimation of Parallel Complexity with Rewriting Techniques[END_REF], we propose a new notion of Parallel Dependency Tuples that capture such a behaviour, and a method to compute parallel complexity bounds.

Parallel-innermost Term Rewriting

The following definitions are mostly standard [START_REF] Baader | Term rewriting and all that[END_REF].

▶ Definition 1 (Term rewrite system, innermost rewriting). T (Σ, V) denotes the set of terms over a finite signature Σ and the set of variables V. For a term t, the set Pos(t) of its positions is defined inductively as a set of strings of positive integers: (a) if t ∈ V, then Pos(t) = {ε}, and (b

) if t = f (t 1 , . . . , t n ), then Pos(t) = {ε} ∪ 1≤i≤n {iπ | π ∈ Pos(t i )}.
The position ε is called the root position of term t. The (strict) prefix order < on positions is the strict partial order given by: π < τ iff there exists π ′ ̸ = ε such that ππ ′ = τ . For π ∈ Pos(t), t| π is the subterm of t at position π, and we write t[s] π for the term that results from t by replacing the subterm t| π at position π by the term s.

For a term t, V(t) is the set of variables in t. If t has the form

f (t 1 , . . . , t n ), root(t) = f is the root of t. A term rewrite system (TRS) R is a set of rules {ℓ 1 → r 1 , . . . , ℓ n → r n } with ℓ i , r i ∈ T (Σ, V), ℓ i ̸ ∈ V, and V(r i ) ⊆ V(ℓ i ) for all 1 ≤ i ≤ n. The rewrite relation of R is s → R t iff
there are a rule ℓ → r ∈ R, a position π ∈ Pos(s), and a substitution σ such that s = s[ℓσ] π and t = s[rσ] π . Here, σ is called the matcher and the term ℓσ is called the redex of the rewrite step. If ℓσ has no proper subterm that is also a possible redex, ℓσ is an innermost redex, and the rewrite step is an innermost rewrite step denoted by

s i → R t. Σ R d = {f | f (ℓ 1 , . . . , ℓ n ) → r ∈ R} and Σ R c = Σ \ Σ R
d are the defined and constructor symbols of R. We may omit the superscript and just write Σ d and Σ c if R is not of importance or clear from the context. Finally, let Pos

d (t) = {π | π ∈ Pos(t), root(t| π ) ∈ Σ d }.
The notion of parallel-innermost rewriting dates back at least to [START_REF] Vuillemin | Correct and optimal implementations of recursion in a simple programming language[END_REF]. Informally, in a parallel-innermost rewrite step, all innermost redexes are rewritten simultaneously. This corresponds to executing all function calls in parallel on a machine with unbounded parallelism.

▶ Definition 2 (Parallel-innermost rewriting [START_REF] Fernández | Orderings for innermost termination[END_REF]). A term s rewrites innermost in parallel to t with a TRS R, written

s i -→ ∥ R t, iff s i -→ + R t,
≤ k ≤ n either s k i -→ ∥ R t k or s k = t k is a normal form.
▶ Example 3 (size). Consider the TRS R with the following rules modelling the code of Figure 1. Note that in the second and in the third step, two innermost steps each are happening in parallel. A corresponding regular innermost rewrite sequence without parallel evaluation of redexes would have needed two more steps.

3

Finding Upper Bounds for Parallel Complexity

Notion of Parallel Complexity

We extend the notion of innermost runtime complexity to parallel-innermost rewriting.

▶ Definition 4 ((Parallel) Innermost Runtime Complexity). The size |t| of a term t is |x| = 1 if x ∈ V and |f (t 1 , . . . , t n )| = 1 + n i=1 |t i |, otherwise. The derivation height of a term t w.r.t. a relation → is the length of the longest sequence of →-steps from t: dh(t, →) = sup{e | ∃ t ′ ∈ T (Σ, V). t → e t ′ } where → e is the e th iterate of →. If t starts an infinite →-sequence, we write dh(t, →) = ω. A term f (t 1 , . . . , t k ) is basic (for a TRS R) iff f ∈ Σ R d and t 1 , . . . , t k ∈ T (Σ R c , V). T R basic is the set of basic terms for a TRS R. For n ∈ N, we define the innermost runtime complexity function irc R (n) = sup{dh(t, i → R ) | t ∈ T basic , |t| ≤ n} and we introduce the parallel innermost runtime complexity function irc ∥ R (n) = sup{dh(t, i -→ ∥ R ) | t ∈ T basic , |t| ≤ n}.
In the following, given a TRS R, our goal shall be to infer (asymptotic) upper bounds for irc ∥ R fully automatically. As usual for runtime complexity, we are considering only basic terms as start terms, corresponding to a defined function called on data objects as arguments. An upper bound for (sequential) irc R is also an upper bound for irc ∥ R . We will introduce techniques to find upper bounds for irc ∥ R that are strictly tighter than these trivial bounds.

Complexity: the sequential case

We build on the Dependency Tuple framework [START_REF] Noschinski | Analyzing innermost runtime complexity of term rewriting by dependency pairs[END_REF], originally introduced to determine upper bounds for (sequential) innermost runtime complexity. A central idea is to group all function calls by a rewrite rule together rather than to regard them separately (as for termination [START_REF] Arts | Termination of term rewriting using dependency pairs[END_REF]).

▶ Definition 5 (Sharp Terms T ♯ ). For every f ∈ Σ d , we introduce a fresh symbol f ♯ of the same arity. For a term t

= f (t 1 , . . . , t n ) with f ∈ Σ d , we define t ♯ = f ♯ (t 1 , . . . , t n ) and let T ♯ = {t ♯ | t ∈ T (Σ, V), root(t) ∈ Σ d }.
To compute an upper bound for sequential complexity, we "count" how often each rewrite rule is used. The idea is that the cost of the function call to the lhs of a rule is 1 + the sum of the costs of all the function calls in the rhs, counted separately. To group k function calls together, we use "compound symbols" Com k , which intuitively represent the sum of the runtimes of their arguments. Then, we can use polynomial interpretations Pol with

Pol(Com k (x 1 , . . . , x k )) = x 1 + • • • + x k for all k to compute a complexity bound [5, Thm. 27].
▶ Definition 6 (Dependency Tuple, DT [START_REF] Noschinski | Analyzing innermost runtime complexity of term rewriting by dependency pairs[END_REF]). A dependency tuple (DT) is a rule of the form

s ♯ → Com n (t ♯ 1 , . . . , t ♯ n ) where s ♯ , t ♯ 1 , . . . , t ♯ n ∈ T ♯ . Let ℓ → r be a rule with Pos d (r) = {π 1 , . . . , π n } and π 1 ◁ . . . ◁ π n for a total order ◁ on positions. Then DT (ℓ → r) = ℓ ♯ → Com n (r| ♯ π1 , . . . , r| ♯ πn ). For a TRS R, let DT (R) = {DT (ℓ → r) | ℓ → r ∈ R}.
▶ Example 7. For our running example, we get the following DTs:

plus ♯ (Zero, y) → Com 0 plus ♯ (S(x), y) → Com 1 (plus ♯ (x, y)) size ♯ (Nil) → Com 0 size ♯ (Tree(v, l, r)) → Com 3 (size ♯ (l), size ♯ (r), plus ♯ (size(l), size(r)))
The following polynomial interpretation, which orients all DTs with ≻ and all rules from R with ≿,

proves irc R (n) ∈ O(n 2 ): Pol(plus ♯ (x 1 , x 2 )) = Pol(size(x 1 )) = x 1 , Pol(size ♯ (x 1 )) = 2x 1 + x 2 1 , Pol(plus(x 1 , x 2 )) = x 1 + x 2 , Pol(Tree(x 1 , x 2 , x 3 )) = 1 + x 2 + x 3 , Pol(S(x 1 )) = 1 + x 1 , Pol(Zero) = Pol(Nil) = 1.
Pol is indeed strictly decreasing along rules (proving termination) and for any term t, Pol(t) ∈ O(|t|).

Computing Upper Bounds for Parallel Rewriting

To find upper bounds for runtime complexity of parallel-innermost rewriting, we can reuse the notion of DTs from Def. 6 for sequential innermost rewriting along with existing techniques [START_REF] Noschinski | Analyzing innermost runtime complexity of term rewriting by dependency pairs[END_REF] and implementations. We illustrate this in the following example.

▶ Example 8. In the recursive size-rule, the two calls to size(l) and size(r) happen in parallel (this will be captured by the notion of structural independency). Thus, the cost for these two calls is not the sum, but the maximum of the calls. Regardless of which of these two calls has the higher cost, we still need to add the cost for the call to plus, which starts evaluating only after both calls to size have finished. With σ as the used matcher for the rule, we have: dh(size(Tree(v, l, r))σ, i -→ ∥ R ) = 1 + max(dh(size(l)σ, i -→ ∥ R ), dh(size(r)σ, i -→ ∥ R )) + dh(plus(size(l), size(r))σ, i -→ ∥ R ) Equivalently, we can "factor in" the cost of calling plus into the maximum function:

dh(size(Tree(v, l, r))σ, i -→ ∥ R ) = max(1 + dh(size(l)σ, i -→ ∥ R ) + dh(plus(size(l), size(r))σ, i -→ ∥ R ), 1 + dh(size(r)σ, i -→ ∥ R ) + dh(plus(size(l), size(r))σ, i -→ ∥ R ))
Intuitively, this would correspond to evaluating plus(size(l), size(r)) twice, in two parallel threads of execution, which costs the same amount of time as evaluating plus(size(l), size(r)) once. We can represent this maximum of the execution times of two threads by introducing two DTs for our recursive size-rule:

size ♯ (Tree(v, l, r)) → Com 2 (size ♯ (l), plus ♯ (size(l), size(r))) size ♯ (Tree(v, l, r)) → Com 2 (size ♯ (r), plus ♯ (size(l), size(r)))
To express the cost of a concrete rewrite sequence, we would non-deterministically choose the DT that corresponds to the "slower thread".

Alternatively, one could introduce a new symbol ComPar k that would be interpreted as the maximum of its arguments:

size ♯ (Tree(v, l, r)) → Com 2 (ComPar 2 (size ♯ (l), size ♯ (r)), plus ♯ (size(l), size(r)))
However, we would then have to extend the notion of Dependency Tuples and also adapt all existing techniques in the Dependency Tuple Framework to work with ComPar k . (Here, unfortunately plus ♯ must wait for size ♯ to finish, so it cannot be evaluated in parallel, and we still need Com 2 to count it in addition to the size ♯ calls.)

In other words, the cost of the function call to the lhs of a rule is 1 + the sum of the costs of all the function calls in the rhs that are in structural dependency with each other. The actual cost of the function call to the lhs in a concrete rewrite sequence is the maximum of all the possible costs of such chains (in the prefix order < on positions) of structural dependency. Thus, structurally independent function calls are considered in separate DTs, whose non-determinism models the parallelism of these function calls.

The notion of structural dependency of functions calls is captured by Def. 9. Basically, it comes from the fact that a term cannot be evaluated before all its subterms have been reduced to normal forms (innermost rewriting/call by value).

▶ Definition 9 (Structural dependency). Let t be a term and τ 1 , τ 2 be the positions of two redexes in t. Let t 1 = t| τ1 and t 2 = t| τ2 . Then t 1 structurally depends on t 2 iff. τ 1 < τ 2 in the prefix order < (i.e., t 2 is a subterm of t 1 ).

In particular, for any rule ℓ → r ∈ R, any substitution σ and any two positions

τ 1 , τ 2 ∈ Pos d (r), r| τ1 structurally depends on r| τ2 iff. τ 1 < τ 2 .
We thus revisit the notion of DTs, which now embed structural dependencies.

▶ Definition 10 (Parallel Dependency Tuples DT ∥ , PDTs). For a rewrite rule ℓ → r, we define the set of its Parallel Dependency Tuples (PDTs)

DT ∥ (ℓ → r): if Pos d (r) = ∅, then DT ∥ (ℓ → r) = {ℓ ♯ → Com 0 }; otherwise, DT ∥ (ℓ → r) = {ℓ ♯ → Com k (r| ♯ π1 , . . . , r| ♯ π k ) | k > 0, π 1 > • • • > π k is a maximal structural dependency chain in Pos d (r)}, where π 1 > • • • > π k is a maximal structural dependency chain in Pos d (r) iff. ∀π ∈ Pos d (r), π ≯ π 1 ∧ π k ≯ π. For a TRS R, let DT ∥ (R) = ℓ→r∈R DT ∥ (ℓ → r).
▶ Example 11. For our recursive size-rule lhs → rhs, we have Pos d (rhs) = {1, 11, 12}. The two maximal >-chains are 11 > 1 and 12 > 1. With rhs| 1 = plus(size(l), size(r)), rhs| 11 = size(l), and rhs| 12 = size(r), we get the PDTs from Ex. 8.

To connect PDTs with our parallel-innermost rewrite relation i -→ ∥ R , we need the notion of chain tree, which is an extension of dependency chains [START_REF] Arts | Termination of term rewriting using dependency pairs[END_REF], and its complexity.

▶ Definition 12 (Chain Tree, Cplx [START_REF] Noschinski | Analyzing innermost runtime complexity of term rewriting by dependency pairs[END_REF]). Let D be a set of DTs and R be a TRS. Let T be a (possibly infinite) tree whose nodes are labelled with a DT from D and a substitution. Let the root node be labelled with (s ♯ → Com n (. . .) | σ). Then T is a (D, R)-chain tree for s ♯ σ iff. the following conditions hold for any node of T , where

(u ♯ → Com m (v ♯ 1 , . . . , v ♯ m ) | µ)
is the label of the node: Let S ⊆ D and s ♯ ∈ T ♯ . For a chain tree T , |T | S ∈ N∪{ω} is the number of nodes in T labelled with a DT from S. We define Cplx ⟨D,S,R⟩ (s ♯ ) = sup{|T | S | T is a (D, R)-chain tree for s ♯ }. For terms s ♯ without a (D, R)-chain tree, we define Cplx ⟨D,S,R⟩ (s ♯ ) = 0.

u ♯ µ
We can now make our main correctness claim:

▶ Proposition 13 (Cplx bounds Derivation Height for i -→ ∥ R ). Let R be a TRS, let t = f (t 1 , . . . , t n ) ∈ T (Σ, V) such that all t i are in normal form. Then we have dh(t, i -→ ∥ R ) ≤ Cplx ⟨DT ∥ (R),DT ∥ (R),R⟩ (t ♯ ). If i -→ ∥ R is confluent, then dh(t, i -→ ∥ R ) = Cplx ⟨DT ∥ (R),DT ∥ (R),R⟩ (t ♯ ).
Thus, in particular we can use polynomial interpretations in the DT framework for our PDTs to get upper bounds for irc ∥ R .

▶ Example 14 (Ex. 8 continued). For our TRS R computing the size function on trees, we get the set DT ∥ (R) with the following PDTs:

plus ♯ (Zero, y) → Com 0 size ♯ (Nil) → Com 0 plus ♯ (S(x), y) → Com 1 (plus ♯ (x, y)) size ♯ (Tree(v, l, r)) → Com 2 (size ♯ (l), plus ♯ (size(l), size(r))) size ♯ (Tree(v, l, r)) → Com 2 (size ♯ (r), plus ♯ (size(l), size(r)))
The interpretation Pol from Ex. 7 implies irc

∥ R (n) ∈ O(n 2
). This bound is tight: consider size(t) for a comb-shaped tree t where the first argument of Tree is always Zero and the third is always Nil. The function plus, which needs time linear in its first argument, is called linearly often on data linear in the size of the start term. Due to the structural dependencies, these calls do not happen in parallel (so call k + 1 to plus must wait for call k).

▶ Example 15. Note that irc ∥ (n) can be asymptotically lower than irc(n), for instance in:

Conclusion

We have come up with a notion of parallel runtime complexity and a concrete algorithm to compute upper bounds on this complexity on TRSs. Future work includes practical design of parallel rewriting engines that infer rewriting schedules from parallel dependency tuples, as well as the formalisation of complexity w.r.t. term height (considering terms as trees), which seems to be more practical for our parallelisation needs.

Figure 1

 1 Figure 1 Tree size computation in Rust

  plus(Zero, y) → y size(Nil) → Zero plus(S(x), y) → S(plus(x, y)) size(Tree(v, l, r)) → S(plus(size(l), size(r))) Here Σ R d = {plus, size} and Σ R c = {Zero, S, Nil, Tree}. We have the following parallel innermost rewrite sequence, where innermost redexes are underlined: size(Tree(Zero, Nil, Tree(Zero, Nil, Nil))) i -→ ∥ R S(plus(size(Nil), size(Tree(Zero, Nil, Nil)))) i -→ ∥ R S(plus(Zero, S(plus(size(Nil), size(Nil))))) i -→ ∥ R S(plus(Zero, S(plus(Zero, Zero)))) i -→ ∥ R S(plus(Zero, S(Zero))) i -→ ∥ R S(S(Zero))

  doubles(Zero) → Nil d(Zero) → Zero doubles(S(x)) → Cons(d(S(x)), doubles(x)) d(S(x)) → S(S(d(x)))The upper bound irc R (n) ∈ O(n 2 ) is tight: from a term doubles(S(S(. . . S(Zero) . . .))), we get linearly many calls of the linear-time function d on arguments of size linear in the start term. However, the Parallel Dependency Tuples in this example are:doubles ♯ (Zero) → Com 0 d ♯ (Zero) → Com 0 doubles ♯ (S(x)) → Com 1 (d ♯ (S(x))) d ♯ (S(x)) → Com 1 (d ♯ (x)) doubles ♯ (S(x)) → Com 1 (doubles ♯ (x))Then the following polynomial interpretation, which orients all DTs with ≻ and all rules from R with ≿, proves irc ∥ R ∈ O(n): Pol(doubles ♯ (x 1 )) = Pol(d(x 1 )) = 2x 1 , Pol(d ♯ (x 1 )) = x 1 , Pol(doubles(x 1 )) = Pol(Cons(x 1 , x 2 )) = Pol(Zero) = Pol(Nil) = 1, Pol(S(x 1 )) = 1 + x 1 .

  and either (a) s i → R t with s an innermost redex, or (b) s = f (s 1 , . . . , s n ), t = f (t 1 , . . . , t n ), and for all 1

  is in normal form w.r.t. R; if this node has the children (p ♯ 1 → Com m1 (. . .) | δ 1 ), . . . , (p ♯ k → Com m k (. . .) | δ k ), then there are pairwise different i 1 , . . . , i k ∈ {1, . . . , m} with v ♯

	ij µ i -→ *	R p ♯ j δ j for all
	j ∈ {1, . . . , k}.

* This work was partially funded by the French National Agency of Research in the CODAS Project (ANR-17-CE23-0004-01).


domain: sde spi chim

text:
Rania Elshypany

Hanaa Selim

K Zakaria

Ahmed H Moustafa

Sadeek A Sadeek

S I Sharaa

Patrice Raynaud

Amr A Nada
email: amr.nada@epri.sci.eg

Zakaria

S I Shara

Elaboration of Fe3O4/ZnO nanocomposite with highly performance photocatalytic activity for degradation methylene blue under visible light irradiation

Keywords: Magnetite, zinc oxide, water remediation, photocatalysis and Photo-degradation

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In recent decades, water contamination has become one of the dominant problems [START_REF] El-Maghrabi | Magnetic graphene based nanocomposite for uranium scavenging[END_REF][START_REF] Ali | High Surface Area Mesoporous Silica for Hydrogen Sulfide Effective Removal[END_REF][START_REF] Najem | Palladium/Carbon Nanofibers by Combining Atomic Layer Deposition and Electrospinning for Organic Pollutant Degradation[END_REF].

One of the harmful compounds in water is methylene blue (MB) [START_REF] Nas | Synthesis, characterization, kinetics and adsorption properties of Pt-Co@GO nano-adsorbent for methylene blue removal in the aquatic mediums using ultrasonic process[END_REF][START_REF] Deng | Adsorption of methylene blue on adsorbent materials produced from cotton stalk[END_REF][START_REF] Nada | Functionalization of MCM-41 with titanium oxynitride deposited via PECVD for enhanced removal of methylene blue[END_REF]. MB is a cationic dye used in different applications as the wood and textile industries [START_REF] Nas | Synthesis, characterization, kinetics and adsorption properties of Pt-Co@GO nano-adsorbent for methylene blue removal in the aquatic mediums using ultrasonic process[END_REF][START_REF] Deng | Adsorption of methylene blue on adsorbent materials produced from cotton stalk[END_REF]. In industry, the remediation of water from MB is a major problem, as failure to removal it has led to hazards in living organisms and the environment. Recently, various techniques for MB removal in aqueous media have been developed such as adsorption [START_REF] Nada | Functionalization of MCM-41 with titanium oxynitride deposited via PECVD for enhanced removal of methylene blue[END_REF][START_REF] Medhat | Efficiently activated carbons from corn cob for methylene blue adsorption[END_REF], biosorption mechanism [START_REF] Nas | Synthesis, characterization, kinetics and adsorption properties of Pt-Co@GO nano-adsorbent for methylene blue removal in the aquatic mediums using ultrasonic process[END_REF], membrane [START_REF] Zhao | Highly flexible magnesium silicate nanofibrous membranes for effective removal of methylene blue from aqueous solution[END_REF], Fenton [START_REF] Liu | Synergetic degradation of Methylene Blue through photocatalysis and Fenton reaction on two-dimensional molybdenite-Fe[END_REF] and photocatalytic process [START_REF] Nada | Mesoporous ZnFe2O4@TiO2 nanofibers prepared by electrospinning coupled to PECVD as highly performing photocatalytic materials[END_REF]. Most of the normal techniques for MB removal have limitations, as they result in secondary pollutants like adsorption and biosorption mechanism, or they are expensive such as the membrane process [START_REF] Nada | Mesoporous ZnFe2O4@TiO2 nanofibers prepared by electrospinning coupled to PECVD as highly performing photocatalytic materials[END_REF]. However, the photocatalytic technique for the degradation of hazardous substance becomes significant [START_REF] Morshedy | Highly efficient Imprinted Polymer Nanocomposites for photocatalytic desulfurization of real diesel fuel[END_REF][START_REF] Rehan | Development of multifunctional polyacrylonitrile/silver nanocomposite films: Antimicrobial activity, catalytic activity, electrical conductivity, UV protection and SERS-active sensor[END_REF][START_REF] Tantawy | Novel synthesis of bimetallic Ag-Cu nanocatalysts for rapid oxidative and reductive degradation of anionic and cationic dyes[END_REF], due to its unique advantages without producing secondary pollutants. The photocatalyst degrades the harmful substance into friendly components as carbon dioxide and water [START_REF] El-Maghrabi | Construction of a new ternary α-MoO3-WO3/CdS solar nanophotocatalyst towards clean water and hydrogen production from artificial wastewater using optimal design methodology[END_REF][START_REF] El-Maghrabi | One pot environmental friendly nanocomposite synthesis of novel TiO2-nanotubes on graphene sheets as effective photocatalyst[END_REF]. Specially, when the photocatalyst has magnetic properties, it is easy to be utilized for several times.

Over the past years, researchers in the major of water treatment have focused on the improvement of nano materials which act as photocatalysts [START_REF] Diab | Facile fabrication of NiTiO3/graphene nanocomposites for photocatalytic hydrogen generation[END_REF][START_REF] El-Maghrabi | Coaxial nanofibers of nickel/gadolinium oxide/nickel oxide as highly effective electrocatalysts for hydrogen evolution reaction[END_REF][START_REF] Kawrani | Enhancement of calcium copper titanium oxide photoelectrochemical performance using boron nitride nanosheets[END_REF][START_REF] Nada | Highly textured boron/nitrogen co-doped TiO2 with honeycomb structure showing enhanced visible-light photoelectrocatalytic activity[END_REF][START_REF] Nada | A novel photoelectrode of NiO@ZnO nanocomposite prepared by Pechini method coupled with PLD for efficiency enhancement in[END_REF][START_REF] El-Maghrabi | Photocorrosion resistant Ag2CO3@Fe2O3/TiO2-NT nanocomposite for efficient visible light photocatalytic degradation activities[END_REF][START_REF] El-Maghrabi | Synthesis of mesoporous core-shell CdS@TiO2 (0D and 1D) photocatalysts for solar-driven hydrogen fuel production[END_REF][START_REF] Kawrani | Segregation of copper oxide on calcium copper titanate surface induced by Graphene Oxide for Water splitting applications[END_REF][START_REF] Miquelot | In-and out-plane transport properties of chemical vapor deposited TiO2 anatase films[END_REF][START_REF] Liang | Facile preparation of metallic 1T phase molybdenum selenide as cocatalyst coupled with graphitic carbon nitride for enhanced photocatalytic H2 production[END_REF][START_REF] Qin | Au nanorods decorated TiO2 nanobelts with enhanced full solar spectrum photocatalytic antibacterial activity and the sterilization file cabinet application[END_REF][START_REF] Sun | The fabrication of 1D/2D CdS nanorod@Ti3C2 MXene composites for good photocatalytic activity of hydrogen generation and ammonia synthesis[END_REF]. Several semiconductors such as SnO2, WO3,TiO2, CeO2, and ZnO have been utilized as heterogeneous photocatalysis [START_REF] Herrmann | Heterogeneous photocatalysis: fundamentals and applications to the removal of various types of aqueous pollutants[END_REF][START_REF] Xu | Flower-like ZnO-Ag2O composites: precipitation synthesis and photocatalytic activity[END_REF].

Most of these semiconductors have a wide-band-gap, which requires ultraviolet light to be active [START_REF] Lin | Photocatalytic oxidation of toxic organohalides with TiO2/UV: The effects of humic substances and organic mixtures[END_REF][START_REF] Abo | Optimized photodegradation of Bisphenol A in water using ZnO, TiO2 and SnO2 photocatalysts under UV radiation as a decontamination procedure[END_REF]. Among these semiconductors, ZnO is one of the excellent photocatalytic material because of its high catalytic activity and being environmentally friendly [START_REF] Yu | Hydrothermal synthesis and photocatalytic activity of zinc oxide hollow spheres[END_REF][START_REF] Hariharan | Photocatalytic degradation of organic contaminants in water by ZnO nanoparticles: Revisited[END_REF]. ZnO nanoparticles has a huge surface area and a large number of active sites [START_REF] Li | High Purity Anatase TiO2 Nanocrystals: Near Room-Temperature Synthesis, Grain Growth Kinetics, and Surface Hydration Chemistry[END_REF]. ZnO is classified as an n-type semiconductor [START_REF] Wang | New insights into fluorinated TiO2 (brookite, anatase and rutile) nanoparticles as efficient photocatalytic redox catalysts[END_REF]. It has a wide band gap energy of approximately 3.37 eV [START_REF] Wang | New insights into fluorinated TiO2 (brookite, anatase and rutile) nanoparticles as efficient photocatalytic redox catalysts[END_REF]. The large band gap of ZnO leaded to its excitations in the UV range below 400 nm. The high level of electrons/holes recombination is another restriction associated with ZnO [START_REF] Zhou | Effects of Fe-doping on the photocatalytic activity of mesoporous TiO2 powders prepared by an ultrasonic method[END_REF][START_REF] Estrellan | Effect of Co-doping Nb with Various Transition Metals on the Photocatalytic Activity of Sol-gel Derived TiO2[END_REF]. This deficit can be remediated by modifying ZnO [START_REF] Li | High Purity Anatase TiO2 Nanocrystals: Near Room-Temperature Synthesis, Grain Growth Kinetics, and Surface Hydration Chemistry[END_REF]. This modification enhanced the absorption to be in the visible light irradiation. Moreover, it reduces the rate of recombination between electrons/holes. Therefore, various systems have been implemented to overcome the drawbacks of ZnO, for example, doping, modification of the surface with metal nanoparticles, and the advancement of heterostructure [START_REF] Li | High Purity Anatase TiO2 Nanocrystals: Near Room-Temperature Synthesis, Grain Growth Kinetics, and Surface Hydration Chemistry[END_REF][START_REF] Thi | Great improvement on tetracycline removal using ZnO rodactivated carbon fiber composite prepared with a facile microwave method[END_REF][START_REF] Akhundi | Ternary magnetic g-C3N4/Fe3O4/AgI nanocomposites: novel recyclable photocatalysts with enhanced activity in degradation of different pollutants under visible light[END_REF]. Among these, the coupling ZnO with p type materials as Fe3O4 can increase the range of light absorption and accelerate the separation rate of the electron-hole pairs [START_REF] Cao | Magnetic photocatalysts with a p-n junction: Fe3O4 nanoparticle and FeWO4 nanowire heterostructures[END_REF]. Thus, the photocatalytic performance of the Fe3O4/ZnO nanocomposite is assumed to be more active due to the electrons/holes separation in the p-n junction [START_REF] El-Maghrabi | Design of Ni/NiO-TiO2/rGO nanocomposites on carbon cloth conductors via PECVD for electrocatalytic water splitting[END_REF]. Moreover, the current magnetic properties make photocatalysts more easy to isolate and reuse from wastewater following the utilization of an external magnet [START_REF] El-Maghrabi | Magnetic graphene based nanocomposite for uranium scavenging[END_REF][START_REF] Nada | Elaboration of nano titania-magnetic reduced graphene oxide for degradation of tartrazine dye in aqueous solution[END_REF][START_REF] Salama | A new way in synthesizing magnetic nano gel for cleaning an Egyptian Coptic fresco painting[END_REF][START_REF] Draz | Large scale hybrid magnetic ZnFe2O4/TiO2 nanocomposite with highly photocatalytic activity for water splitting[END_REF].

There are some scientists interested in fabricating Fe3O4/ZnO in order to enhance its photocatalytic activity through different preparation methods to obtain different structure and morphology. C. Karunakaran and co-workers [START_REF] Karunakaran | Nonquenching of Charge Carriers by Fe3O4 Core in Fe3O4/ZnO Nanosheet Photocatalyst[END_REF] reported that the core-shell of Fe3O4/ZnO nanosheets by hydrothermal synthesis allows the band gap of Fe3O4 to be conjugated inside the band gap of ZnO for 98.5 %, 25% photodegradation of 25 ppm methylene blue under UV and visible light, respectively. The core-shell structure has a limited activity under visible light than UV source. Also, the core-shell structure of Fe3O4/ZnO was studied by M. Nikazar et al. [START_REF] Nikazar | The optimum conditions for synthesis of Fe3O4/ZnO core/shell magnetic nanoparticles for photodegradation of phenol[END_REF] for phenol photodegradation to obtain a removal rate of 88% under UV irradiation. However, the same structure of core-shell was synthesized by Q. Feng et al. [START_REF] Feng | Synthesis and characterization of Fe3O4/ZnO-GO nanocomposites with improved photocatalytic degradation methyl orange under visible light irradiation[END_REF], then enhance it by graphene oxide to be active under visible illumination for the degradation of methyl orange. Furthermore, O.

Długosz et al. [START_REF] Długosz | Synthesis of Fe3O4/ZnO nanoparticles and their application for the photodegradation of anionic and cationic dyes[END_REF] evaporated Fe3O4/ZnO by microwave process to recorded 63% removal percent of methylene blue. We can conclude that from previous studies the photocatalytic activity of Fe3O4/ZnO depend on the preparation method and the structure of the nanocomposite.

In this study, we demonstrate that Fe3O4/ZnO by the solid-state method is a rapid and easy method with changing the ratio between Fe3O4 and ZnO to get the optimum ratio between them. Among all techniques utilized to synthesize magnetite / zinc oxide, solid state is a cost-effective and simple technique. The crystalline structure, chemical states and morphology of the prepared photocatalyst were characterized by XRD, Raman, FTIR, XPS and TEM techniques. Furthermore, the optical properties were investigated by photoluminescence and UV-Vis spectroscopies.

Finally, the photocatalytic activity of Fe3O4/ZnO nanocomposite was detected by degradation of methylene-blue (MB) under visible light illumination and with different conditions as an applied trapping agent. Moreover, the prepared photocatalyst has high efficiency for easy extraction and reuse again.

Experimental

Nanoparticle synthesis

Synthesis of ZnO nanoparticles (Z)

ZnO nanoparticles (ZnO NPs) were synthesized by precipitation method [START_REF] Li | Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency[END_REF]. 6mM of Zn (NO3)2.6H2O was dissolved in 25 mL distilled water with stirring for 30 minutes at 100 o C. The pH value was adjusted at 12 by using 1M NaOH and stirring it for 1 h. The white precipitate was collected by centrifugation at a speed of 4000 rpm. The obtained precipitate was washed several times with deionized water and ethanol, then dried at 60 ᵒC for 6 hrs in an electric oven and calcined at 600 o C for 2hrs in air.

Synthesis of Fe3O4 magnetics nanoparticles (M)

Fe3O4 magnetic nanoparticles (Fe3O4 NPs) were prepared via co-precipitation method. We used ferrous and ferric salts in a ratio of 1:2 M ratio in the presence of N2 gas as recorded in our previous study [START_REF] Nada | Elaboration of nano titania-magnetic reduced graphene oxide for degradation of tartrazine dye in aqueous solution[END_REF]. The relevant chemical reaction can be expressed as follows:

Fe 2+ + 2Fe 3+ + 8OH -→ Fe3O4 + 4H2O (eq.1)

Synthesis of Fe3O4/ZnO nanocomposites (MZ) by solid state method

MZ was prepared by thermolysis process and calcination at 600 o C for 4 h by solid state method [START_REF] Kawrani | Enhancement of calcium copper titanium oxide photoelectrochemical performance using boron nitride nanosheets[END_REF][START_REF] Kawrani | Segregation of copper oxide on calcium copper titanate surface induced by Graphene Oxide for Water splitting applications[END_REF][START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF]. With different weight ratios of M:Z (0.2:1, 0.4:1, 0.6: 1, 0.8:1 and 1:1 wt.%) and donated as MZ1, MZ2, MZ3, MZ4, and MZ5, respectively.

Characterization

The phase of the prepared samples was examined by X-ray diffraction (XRD) using a diffractometer (Panalytical XPERT PRO MPD). CuKα radiation (λ=1.5418 Å) was used at 40 kV and 40 mA. The morphology was investigated by transmission electron microscope (TEM) model JEM-2100, JEOL, Japan. The structural study of the prepared samples was investigated by Raman spectroscopy with a 532 nm laser source and a power of 10 mW (model Sentera, Bruker, Germany). The functional groups were identified by a Fourier transform infrared spectrometer (FT-IR) model spectrum one (Perkin Elmer, USA) in the wave number range of 400 -4000 cm -1 .

The optical reflectance was recorded by a UV-Vis spectrometer (Perkin Elmer Lambda 1050).

Photoluminescence spectra were recorded by a Cary Eclipse Fluorescence Spectrophotometer.

Photocatalytic activity study

The photocatalytic activity of MZ1, MZ2, MZ3, MZ4, and MZ5 nanocomposites was studied through the degradation of methylene blue (MB). MB was used as an organic pollutants reference in aqueous solution. The photocatalytic activity was detected under visible illumination of a halogen lamp (500 W/cm 2 ) placed 10 cm above the 4 cm diameter reactor tube. First, 0.2 g of prepared samples were suspended in 50 mL of aqueous methylene blue solution at a concentration of 100 ppm. The mixture was stirred for 30 min in a dark box, until adsorption-desorption equilibrium was obtained between MB dye and nanocomposite (photocatalyst) before light irradiation. Then, 3mL of the suspensions were withdrawn regularly from reactor and centrifuged to remove the catalyst. The clean centrifuged solutions were analysed by UV-vis spectrophotometer [START_REF] Nada | Elaboration of nano titania-magnetic reduced graphene oxide for degradation of tartrazine dye in aqueous solution[END_REF].

Results and discussion

Magnetite and zinc oxide were elaborated with different ratios to form a homogeneous nanocomposite. X-ray diffraction (XRD) was used for detecting the crystalline phase of M, Z, MZ1, MZ2, MZ3, MZ4 and MZ5 as presented in Figure 1 400), ( 422), (511), and (440), respectively [START_REF] Li | Kinetics of adsorption of Saccharomyces cerevisiae mandelated dehydrogenase on magnetic Fe3O4-chitosan nanoparticles[END_REF]. These peaks are attributed to the cubic spinal structured magnetite. No significant peaks corresponding to impurities were detected in the XRD pattern. After mixing Fe3O4 NPs with ZnO, peaks of both magnetite and zinc oxide are detected. In the nanocomposite, some intensities of the peaks changed due to peak interference. The Raman spectra of all prepared samples are shown in Figure 2. The normal vibrational modes of ZnO have A1+2E2+2B1+E1 [START_REF] Arguello | First-order Raman effect in wurtzite-type crystals[END_REF], where A1 and E1 consist of two modes: Longitudinal Optical (LO) and Transverse Optical (TO). B1 is inactive Raman. E2 consists of two modes: high frequency phonon E2H and low frequency phonon E2L [START_REF] Cuscó | Temperature dependence of Raman scattering in ZnO[END_REF]. The peak at 435.5 cm -1 in the Raman spectrum of Z sample is assigned to E2H mode of ZnO (the strongest mode). The peak at 328 cm -1 assigned to A1T. And the peak at 576 cm -1 is assigned to A1L (longitudinal optical (LO) mode).

Nonetheless the A1L phonon peak of bulk ZnO showed reached 574 cm -1 [START_REF] Ashkenov | Infrared dielectric functions and phonon modes of high-quality ZnO films[END_REF]. In contrast, the M sample (Fe3O4) has peaks at 218.5, 282, 396 and 652.5 cm -1 and they correspond to A1g, Eg, Eg and A1g, respectively [START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF][START_REF] Mukhtar | Structural characterization of self-assembled chain like Fe-FeOx Core shell nanostructure[END_REF][START_REF] Yew | An eco-friendly means of biosynthesis of superparamagnetic magnetite nanoparticles via marine polymer[END_REF]. Compared with pure ZnO nanocrystals, the A1L mode of the Fe3O4/ZnO nanocomposites appeared in the blue shift at peak 609.9 cm -1 . When the Furthermore, the contributing factor could be the interfacial charge shift between Fe3O4 and ZnO, which was replaced by electrons in the nanocomposite materials were catalysed from the ZnO nanocrystals, then they will expend and absorb into the Fe3O4 nanoparticles. This is followed by recombination with the remaining holes at the ZnO-Fe3O4 interface leading to a frequency shift [START_REF] Zou | Multifunctional Fe3O4/ZnO nanocomposites with magnetic and optical properties[END_REF]. Moreover, the relative intensity of A1T and A1L (ZnO) during the limitation of the ZnO quantity in nanocomposites decreased gradually from MZ1 to MZ5. In addition, the peak cat 1310 cm -1 related to the scattering of two magnon were observed in the nanocomposites due to the presence of scattering generated from the antiparallel spin of two magnons, where the homogeneity and synergism between ZnO and Fe3O4 were confirmed [START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF]. Figure S1 demonstrates the FT-IR spectra of ZnO, Fe3O4 and Fe3O4/ZnO nanocomposite before the degradation of MB, which was performed in the range of 400 -4,000 cm -1 . The characteristic bond of ZnO is well observed at 449 cm -1 . The weak band near 1637.8 cm -1 is attributed to the H-O-H bending vibration due to adsorbed water on the surface of nanoparticles. The broad peak centred around 3400 cm -1 corresponds to the stretching vibration mode of hydroxyl groups ( -OH) [START_REF] Shirzad-Siboni | Photocatalytic reduction of hexavalent chromium over ZnO nanorods immobilized on kaolin[END_REF]. Also, the band at 568 cm -1 is assigned to Fe-O bond vibration mode [START_REF] Sun | Magnetite/reduced graphene oxide nanocomposites: one step solvothermal synthesis and use as a novel platform for removal of dye pollutants[END_REF][START_REF] Wang | Water-soluble Fe3O4 nanoparticles with high solubility for removal of heavy-metal ions from waste water[END_REF]. The FT-IR spectra of Fe3O4/ZnO nanocomposite were identical to the hybridization of ZnO nanocrystals with Fe3O4 [START_REF] Farrokhi | Application of ZnO-Fe3O4 nanocomposite on the removal of azo dye from aqueous solutions: kinetics and equilibrium studies[END_REF], taking into consideration that coupling Fe3O4 with ZnO should to be homogeneous. Furthermore, the chemical composition of Fe3O4/ZnO (MZ4) was detected by X-ray photoelectron spectroscopy analysis (XPS) as presented in Figure 3a-c. The XPS spectra of iron have two peaks of Fe3O4: 2p3/2 and 2p1/2 at 711.5 and 723.7 eV, respectively [START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF][START_REF] Guo | Flowerlike iron oxide nanostructures and their application in microwave absorption[END_REF] (in Figure 3-a) which are matched with XRD and Raman. In addition, the zinc peak at 121 eV corresponds to Zn 2p3/2 which it was bound to ZnO in Figure 3-b [START_REF] Yu | Duality in the mechanism of hexagonal ZnO/CuxO nanowires inducing sulfamethazine degradation under solar or visible light[END_REF]. XPS of oxygen 1s in Figure 3-c at 530.4 eV related to lattice oxygen (OL) [START_REF] Qu | Graphene-modified ZnO nanostructures for low-temperature NO2 sensing[END_REF] in the Fe3O4/ZnO nanocomposite.

Moreover, the morphology of prepared nanocomposites was detected by transmission electron microscopy. TEM images of the Z, M, MZ1, MZ4, and MZ5 nanocomposites are presented in Figure 4a-e. The presence of homogeneous nanocrystalline ZnO particles with spherical shapes and weak agglomeration is observed in Figure 4a) [START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF]. Figure 4b shows the iron

Optical analysis

There are several mechanisms that control photocatalytic activity: the production of electron / hole pairs, photoabsorption, charge / carrier transfer, and charge carrier utilization. The optimization of the photocatalytic activity depends on the efficiency of the product and the transfer of the e -/ h + pairs, which depends on the energy band gap (Eg) of the photocatalyst. The energy band gap values (Eg) of the samples were determined according to the following equations [START_REF] Abo | Optimized photodegradation of Bisphenol A in water using ZnO, TiO2 and SnO2 photocatalysts under UV radiation as a decontamination procedure[END_REF][START_REF] Yu | Hydrothermal synthesis and photocatalytic activity of zinc oxide hollow spheres[END_REF]: 𝛼ℎ𝑣 = 𝐴(ℎ𝑣 -𝐸𝑔) 𝑛/2 (eq.2)

Where α is the absorption coefficient, 𝑣 is the frequency of light and n is the constant of proportionality. The n value is determined by the transition of the semiconductor, i.e., the direct transition as in the prepared nanocomposite (n = 1). The DRS spectra of the prepared ZnO, Fe3O4, MZ1, MZ2, MZ3, MZ4 and MZ5 NPs are shown in figure 5. The band gap value of pure ZnO NP is 3.20 eV. However, the band gap of the Fe3O4/ZnO nanocomposites shifted towards the redshift in the presence of magnetite and there are two bandgaps for all samples according to Table 1. The conjugation of two bands gap led to more stability between the e -/h + pairs. Moreover, Fe3O4/ZnO nanocomposites can be excited under visible light to give more electron-hole pairs. The room temperature photoluminescence (PL) spectra of all prepared samples were shown in Figure 6. PL spectrum of pure ZnO shows a strong emission band at 381 nm. In addition, some peaks at 406 nm, 420 nm and 445 nm appear due to deep level emission (DLE) [START_REF] Oprea | THE INFLUENCE OF THE THERMAL TREATMENT ON LUMINESCENCE PROPERTIES OF ZnO[END_REF]. A strong quenching of PL intensity after incorporation of Fe3O4 with ZnO, indicating that the recombination between photo-electrons generated and holes is reduced.

Photocatalytic activity

The photocatalytic efficiency of the (MZ1, MZ2, MZ3, MZ4 and MZ5) nanocomposites was evaluated for MB under visible light irradiation (wavelength ˃ 400 nm). MB was chosen as an organic pollutant model. Where r is the degradation rate of MB (mg L -1 min -1 ), C is the concentration of the MB solution (mg L -1 ), t is the irradiation time, k is the reaction rate constant (mg L -1 min -1 ), and K is the adsorption coefficient of MB (mg L -1 ). The relationship between ln (C0/C) and the reaction time (t) showed that the decomposition of MB with different photocatalysts follows a pseudo-first-order kinetic Ln (C0/C) =k KT= ka t (eq.4)

Where ka is the apparent first-order rate constant (min -1 ), Co is the concentration at time =0 of irradiation, and C is the concentration at time t.

ka values obtained from the linear relation between ln (C0/C) and time are reported in Table 1 and increased in the following order: MZ4˃MZ3˃MZ2˃MZ5˃MZ1˃ZnO˃MB meaning MZ4 sample shows the best activity. In addition, MZ4 has a higher photocatalytic efficiency under visible light irradiation compared to previous studies Table 2. Beside the kinetic study, an important factor for judging materials is Figure of Merit (FOM). FOM in our case is based on international union of pure and applied chemistry (IUPAC) for photocatalytic process defined as collector area per order (ACO) due to the reaction process follow first order kinetics [START_REF] Bolton | Figures-of-merit for the technical development and application of advanced oxidation technologies for both electric-and solar-driven systems (IUPAC Technical Report)[END_REF][START_REF] Bolton | Figures-of-merit for the technical development and application of advanced oxidation processes[END_REF]. The Figure of Merit (FOM) for all the prepared nanocomposite illustrated in Table 1, where ACO was defined by the following equation:

𝐴 𝑐𝑜 = 𝐴𝐸 ̅ 𝑠 𝑡 𝑉 𝑙𝑜𝑔(𝐶 𝑖 /𝐶 𝐹 ) (eq.5)
Where, A (m 2 ) is the light-exposed area, 𝐸 ̅ 𝑠 is the average solar irradiance (W/m 2 ), t is time of illumination (h), V is volume of reactor (m 3 ), Ci and Cf are the initial and final concertation of pollutant. Furthermore, the equation supposes first order kinetics, so log (Ci/Cf) = 0.434 ka t; where: t is time (h) and ka is the apparent first-order rate constant (h -1 ) [START_REF] Bolton | Figures-of-merit for the technical development and application of advanced oxidation technologies for both electric-and solar-driven systems (IUPAC Technical Report)[END_REF][START_REF] Bolton | Figures-of-merit for the technical development and application of advanced oxidation processes[END_REF]. Equation 4 will be as following:

𝐴 𝑐𝑜 = 𝐴𝐸 ̅ 𝑠 0.434 𝑉𝐾 𝑎 (eq.6)

In addition, the pH-changing during the photodegradation was detected on order to obtain more information about MB photodegradation under different condition for MZ4 as presented in Figure 7.c. The results indicated that the pH of the solution has a changing effect of the MB photodegradation process by MZ4 due to the electrostatic interactions between the substrate, the photocatalyst and the charged produced radicals during the photodegradation process. Therefore, it has been very difficult to illustrate the pH effects of the MB photodegradation. The MB showed in cationic form at pH=5 and MZ4 has negatively charged. Therefore, there is electrostatic attraction between cationic dye and MZ4. However, the best MB photodegradation recorded at pH=6 due to the presence of ideal electrostatic attraction and the ability to the free radical formation on the surface of photocatalyst. Moreover, zinc oxide was the important photocatalyst in MZ4 at that pH [START_REF] Wang | Synthesis of rectorite/Fe3O4/ZnO composites and their application for the removal of methylene blue dye[END_REF]. In addition, the pH effect on (100 ppm) MB degradation in the presence and absence of MZ4 after 2 h of visible light illumination is displayed in Figure S2. Where, MB is bleached under acidic medium without catalysts, but with a low effect not more than 10% when compared with presence of MZ4 at 88.5% removal efficiency. Furthermore, the effect of MB initial concentration was studied on its photodegradation from 50 to 200 ppm as presented in Figure 7.c.

The degradation efficiency decreased with increased the initial concentration of MB due to the limitation of illumination by agglomerated MB on the photocatalyst [START_REF] Nada | Mesoporous ZnFe2O4@TiO2 nanofibers prepared by electrospinning coupled to PECVD as highly performing photocatalytic materials[END_REF][START_REF] Nada | BN/GdxTi(1-x)O(4-x)/2nanofibers for enhanced photocatalytic hydrogen production under visible light[END_REF].

To determine the stability of (MZ4) Fe3O4/ZnO nanocomposite photocatalyst, recycling tests for the degradation of MB under visible light were performed on the photocatalyst, which are presented in Figure 7.d. The photocatalyst was collected by magnet then it was washed with distilled water and ethanol. IR characteristics were examined before and after photocatalytic degradation in Figure S3. Where, the same function groups have been observed in the catalyst before and after photocatalytic degradation. Thus, the prepared nanocomposite has high recovery and reusability for photocatalytic activity, in addition to studying the roles of free radical. we applied trapping agents of free radical: Tert-butyl alcohol (TBA), p-benzoquinone (BQ) and disodium ethylenediaminetetraacetic acid (Na2-EDTA) to scavenge the hydroxyl radicals, superoxide radicals and holes, respectively as present in Figure 7.d [START_REF] Fan | Synthesis of metal-phase-assisted 1T@ 2H-MoS2 nanosheet-coated black TiO2 spheres with visible light photocatalytic activities[END_REF]. The removal efficiency of MB changed dependent on the sacrificial agents, and the removal efficiency decreased to 39% in the presence of (5mM) TBA as hydroxyl radicals played an important role in the photodegradation of MB. The degradation mechanism based on all previous results and the energy band of hereto structure of magnetite ZnO is shown in Figure 8. When ZnO and Fe3O4 are coupled together, photons may be absorbed in both ZnO and Fe3O4 and form the electron/hole pairs. Where, ZnO and Fe3O4 have a positions of conduction bands (-0.45 eV and -0.58 eV vs NHE) and valence bands (+ 2.75 eV and + 0.99 eV vs NHE), respectively [START_REF] Zhu | Photocatalytic degradation of polyacrylamide by rGO@Fe3O4/Cu2O@ZnO magnetic recyclable composites[END_REF][START_REF] Talukdar | Novel Z-scheme Ag3PO4/Fe3O4-activated biochar photocatalyst with enhanced visible-light catalytic performance toward degradation of bisphenol A[END_REF]. The electrons of the conduction Band (CB) of Fe3O4 would migrate to that of the ZnO. Whereas holes at the valence Band (VB) of Fe3O4 would remain there. This process reduces the probability of the electron/hole recombination. Therefore, there is an enhancement of photocatalytic activities of the Fe3O4/ZnO compared to the pure ZnO. After that the OH -present in the aqueous solution is captured by the hole of the valence band to form highly reactive OH . Radical. Then, the dye molecules attacked by this radical are decomposed into simple products [START_REF] Abo-Farha | Photocatalytic degradation of monoazo and diazo dyes in wastewater on nanometer-sized TiO2[END_REF][START_REF] Shanthi | Photocatalytic degradation of an azo dye, Acid Red 27, in aqueous solution using nano ZnO[END_REF]. This can be described by the following steps:

1) Photoexcitation

Photoelectron is transfered from valence band (filled) of a semiconductor to conduction band (empty).

2) Ionization of water

Holes in the valence band react with water to produce OH . radical

3) Oxygen ionosorption

Electron in conduction band is taken by oxygen to produce superoxide radical O2 .- Fe3O4/ZnO Fe3O4/ZnO (h + ) +Fe3O4/ZnO (e -) (eq.7)

Fe3O4/ZnO (e -) + O2 O2 .- (eq.8)

Fe3O4/ZnO (h + ) +H2O

OH . + H + (eq.9)

H2O + O2 .- 2 . OH (eq.10)

. OH + MB degredation products (eq.11)

Figure 8. Schematic diagram of the MZ4 photocatalytic activity mechanism.

Conclusion

The Fe3O4/ZnO nanocomposite was successfully synthesized by a solid-state process under the optimal conditions achieved at 600 o C for 4 h with different ratios between Fe3O4 and ZnO.

The XRD, XPS, TEM, Raman and FT-IR spectroscopy measurement contributed to the understanding of the structural phase of Fe3O4/ZnO nanocomposites. All characterization techniques confirmed the strong incorporation between Fe3O4 and ZnO compounds, which consequently enhanced the band-gap for the nanocomposites that were recorded by UV-DRs to be active under visible light illumination. Furthermore, the heterogenous band gap between Fe3O4

and ZnO quenched the Photoluminescence and improved the life time of e -/h + . Photocatalytic activity measurements of different coupling of Fe3O4 with ZnO led to better activity in the degradation of MB under visible light. The highest degradation efficiency (88.5 %) was reached with sample MZ4 with high stability up to five cycles. In addition, the preferred pH for MB degradation by MZ4 under visible light is 6. The mechanism of MB degradation mainly depends on hydroxyl radical corresponding to the effect of the various trapping agents applied (TBA, BQ and Na2-EDTA). Moreover, the prepared materials have the ability to be easily extracted from the

Figure 1 .

 1 Figure 1. XRD spectra of Z, M, MZ1, MZ2, MZ3, MZ4 and MZ5 nanocomposites.

  through the Fe3O4/ZnO nanocomposites, the polarization of the ZnO component will be strongly influenced by the incorporation with Fe3O4 magnetic nanoparticles. Hence the excited electrode dipoles result in a vibrational frequency shift.

Figure 2 .

 2 Figure 2. Raman spectra of the Z, M, MZ1, MZ2, MZ3, MZ4 and MZ5 nanocomposites.

  a cubic morphology[START_REF] Elshypany | Magnetic ZnO Crystal Nanoparticle Growth on Reduced Graphene Oxide for Enhanced Photocatalytic Performance under Visible Light Irradiation[END_REF][START_REF] Laurent | Magnetic iron oxide nanoparticles: synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications[END_REF] and Figures4c-efor Fe3O4/ZnO composites show the cubic and spherical morphology with average diameter 15 ± 2 nm and 20 ± 4 nm for Fe3O4 and ZnO, respectively as the nanocomposites structure. In addition, the MZ4 nanocomposite has a uniform distribution without accumulation. In addition, the elemental composition of the nanocomposites by EDX presented in TableS1which confirmed the atomic ratio between Fe3O4 and ZnO which is in consistent with the experimental values.

Figure 3 .Figure 4 .

 34 Figure 3. XPS spectra of MZ4 (a) Fe 2P; (b) Zn 2P and (c) O 1S

Figure 5 .

 5 Figure 5. UV-Vis diffuse reflectance spectra of Z, MZ1, MZ2, MZ3, MZ4 and MZ5 nanocomposites.

Figure 6 .

 6 Figure 6. Photoluminescence spectra of Z, MZ1, MZ2, MZ3, MZ4 and MZ5 nanocomposites.

Figure 7 .

 7 a shows the degradation of MB concentration for all the nanocomposites. The MZ4 NCs shows the strongest degradation of MB, implying the highest photocatalytic activity, followed by MZ3, MZ2, MZ5 and MZ1. Figure 7.b, shows the degradation of kinetic linear curves, where the photodegradation reactions follow a Langmuir-Hinshelwood first-order kinetics model as shown in the following equation: R = dC / dt = kKC / (1+KC) (eq.3)

Figure 7 .

 7 Figure 7. (a) Photodegradation and (b) Kinetic of MB by Z, MZ1, MZ2, MZ3, MZ4 and MZ5 nanocomposites for 100 ppm MB under visible light; (c) The pH and MB concentration effect for MB degradation by MZ4 after 2 h of visible light illumination; and (d) The stability cycles and scavenger study effect for MB degradation by MZ4 for 100 ppm MB after 2 h of visible-light illumination.

2.1. Materials

	Zinc nitrate hexahydrate (Zn(NO3)2.6H2O) (98%, CAS Number: 10196-18-6), ferrous
	sulphate heptahydrate (FeSO4.7H2O) with purity (99.5%, CAS Number: 7782-63-0), iron chloride
	hexahydrate (FeCl3.6H2O) (97%, CAS Number: 10025-77-1), methylene blue (MB) (CAS
	Number: 122965-43-9) and sodium hydroxide (NaOH) (98%, CAS Number: 1310-73-2) were
	obtained from Sigma-Aldrich organization. Ethanol was purchased from Honeywell organization
	with high immaculateness of 99.8 %. All purchased compounds were used as received, with no
	further purification.

  , which demonstrates two sets of diffraction peaks. The first set for ZnO is well indexed to hexagonal wurtzite structure (JCPDS

	Card No. 01-080-4199) with the planes (100), (002), (101), (102), (110), (103), (200), (112) and
	(201) corresponding to 2Ɵ = 31.7, 34.4, 36.2, 47.5, 56.5, 62.8, 66.3, 67.9 and 69.0 o , respectively
	[51]. (Give here the signification of 2Ɵ). The preferred growth orientation is along the (101)
	crystallographic direction. The strong sharp peaks suggested that the ZnO NPs were prepared in
	high crystalline [52]. The other set of magnetite Fe3O4 phase (JCPDS Card no. 01-089-1397) with
	diffraction peaks at 30.00, 35.50, 43.14, 53.44, 57.40, and 62.58 o corresponding to Miller indices
	(220), (311), (

Table 1 .

 1 The band gap and kinetic parameters for photocatalytic activities of ZnO, MZ1, MZ2, MZ3, MZ4, and MZ5 NPs.

		80
			Z
		70	MZ1
			MZ2
	Reflectance(%)	30 40 50 60	MZ3 MZ4 MZ5
		20
		10
		300	400	500	600	700	800
				l,nm
	Sample name	Eg (eV)(Fe3O4)	Eg(eV)(ZnO)	Ka (min -1 )	AOC (TW.h/m 3 )
	MB		--	--		2.468E-4 ± 6E-5	563.1
	ZnO		--	3.20		9.217E-4 ±	150.8
						9.582E-5

Table 2 .

 2 Photo catalytic degradation of MB under Visible Light with Various Photocatalysts.

	photocatalyst	Weight of	Concentration	Time(h) Degradation (%) Ref.
		catalyst	of MB (ppm)
		(g/L)

solution by the external magnetic field. In brief, Fe3O4/ZnO nanocomposites are promising photocatalysts for reducing toxic organic pollutants in wastewater.